Final project_Advanced Modelling

Introduction

The objective of this assignment is to to explore two key areas of predictive modeling: classification and advanced regression, applied to student academic performance. In the classification section our goal is to predict the academic status (graduate, dropout, or enrolled) of students based on various socioeconomic, academic, and institutional factors. This could be helpful to identify early indicators of student success or risk of dropout. On its part, the regression analysis will focus on predicting the average grade of students during their first year of university, using the information available in our dataset.

In sum, by implementing statistical and machine learning approaches, we aim to determine which factors most influence student performance. For it, a publicly available dataset from the Instituto Politécnico de Portalegre, Portugal, was used. The dataset contains 4,424 records spanning academic years 2008/2009 to 2018/2019, integrating information from multiple sources, including the Academic Management System (AMS) and macroeconomic data from PORDATA. I consider it a valuable resource for educational analytics, and expect our findings to provide valuable insights for universities and policymakers to improve student retention and academic outcomes.

Load libraries

library(readr)
library(DataExplorer)
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library(tidyverse)
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library(plotly)
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library(GGally)
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library(ggeffects)
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library(MASS)
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library(tidyr)
library(dplyr)
library(ggplot2)
library(nnet)
library(glmnet)
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library(rpart.plot)
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Read dataset

data <- read.csv("data.csv", sep = ";") 
str(data)
## 'data.frame':    4424 obs. of  37 variables:
##  $ Marital.status                                : int  1 1 1 1 2 2 1 1 1 1 ...
##  $ Application.mode                              : int  17 15 1 17 39 39 1 18 1 1 ...
##  $ Application.order                             : int  5 1 5 2 1 1 1 4 3 1 ...
##  $ Course                                        : int  171 9254 9070 9773 8014 9991 9500 9254 9238 9238 ...
##  $ Daytime.evening.attendance.                   : int  1 1 1 1 0 0 1 1 1 1 ...
##  $ Previous.qualification                        : int  1 1 1 1 1 19 1 1 1 1 ...
##  $ Previous.qualification..grade.                : num  122 160 122 122 100 ...
##  $ Nacionality                                   : int  1 1 1 1 1 1 1 1 62 1 ...
##  $ Mother.s.qualification                        : int  19 1 37 38 37 37 19 37 1 1 ...
##  $ Father.s.qualification                        : int  12 3 37 37 38 37 38 37 1 19 ...
##  $ Mother.s.occupation                           : int  5 3 9 5 9 9 7 9 9 4 ...
##  $ Father.s.occupation                           : int  9 3 9 3 9 7 10 9 9 7 ...
##  $ Admission.grade                               : num  127 142 125 120 142 ...
##  $ Displaced                                     : int  1 1 1 1 0 0 1 1 0 1 ...
##  $ Educational.special.needs                     : int  0 0 0 0 0 0 0 0 0 0 ...
##  $ Debtor                                        : int  0 0 0 0 0 1 0 0 0 1 ...
##  $ Tuition.fees.up.to.date                       : int  1 0 0 1 1 1 1 0 1 0 ...
##  $ Gender                                        : int  1 1 1 0 0 1 0 1 0 0 ...
##  $ Scholarship.holder                            : int  0 0 0 0 0 0 1 0 1 0 ...
##  $ Age.at.enrollment                             : int  20 19 19 20 45 50 18 22 21 18 ...
##  $ International                                 : int  0 0 0 0 0 0 0 0 1 0 ...
##  $ Curricular.units.1st.sem..credited.           : int  0 0 0 0 0 0 0 0 0 0 ...
##  $ Curricular.units.1st.sem..enrolled.           : int  0 6 6 6 6 5 7 5 6 6 ...
##  $ Curricular.units.1st.sem..evaluations.        : int  0 6 0 8 9 10 9 5 8 9 ...
##  $ Curricular.units.1st.sem..approved.           : int  0 6 0 6 5 5 7 0 6 5 ...
##  $ Curricular.units.1st.sem..grade.              : chr  "0.0" "14.0" "0.0" "13.428.571.428.571.400" ...
##  $ Curricular.units.1st.sem..without.evaluations.: int  0 0 0 0 0 0 0 0 0 0 ...
##  $ Curricular.units.2nd.sem..credited.           : int  0 0 0 0 0 0 0 0 0 0 ...
##  $ Curricular.units.2nd.sem..enrolled.           : int  0 6 6 6 6 5 8 5 6 6 ...
##  $ Curricular.units.2nd.sem..evaluations.        : int  0 6 0 10 6 17 8 5 7 14 ...
##  $ Curricular.units.2nd.sem..approved.           : int  0 6 0 5 6 5 8 0 6 2 ...
##  $ Curricular.units.2nd.sem..grade.              : chr  "0.0" "13.666.666.666.666.600" "0.0" "12.4" ...
##  $ Curricular.units.2nd.sem..without.evaluations.: int  0 0 0 0 0 5 0 0 0 0 ...
##  $ Unemployment.rate                             : num  10.8 13.9 10.8 9.4 13.9 16.2 15.5 15.5 16.2 8.9 ...
##  $ Inflation.rate                                : num  1.4 -0.3 1.4 -0.8 -0.3 0.3 2.8 2.8 0.3 1.4 ...
##  $ GDP                                           : num  1.74 0.79 1.74 -3.12 0.79 -0.92 -4.06 -4.06 -0.92 3.51 ...
##  $ Academic.status                               : chr  "Dropout" "Graduate" "Dropout" "Graduate" ...

Data cleaning and preprocessing

The first thing I realize is that column names are long and complex, so I decided to make them more manageable by renaming them to shorter, more intuitive names. Here’s a brief description of some of the variables in our dataset, with the newly assigned names:

  1. Demographic Features:

    • marital_status: Marital status of the student.

    • gender: Gender of the student.

    • age_enrollment: Age at enrollment.

    • nationality: Nationality of the student.

  2. Academic Features:

    • prev_qualification: Previous qualification.

    • prev_grade: Grade from previous qualification.

    • admission_grade: Admission grade.

    • course: Course enrolled in.

    • enrolled_1st_sem: Number of courses enrolled in the first semester.

    • approved_1st_sem: Number of courses approved in the first semester.

    • grade_1st_sem: Average grade in the first semester.

    • enrolled_2nd_sem: Number of courses enrolled in the second semester.

    • approved_2nd_sem: Number of courses approved in the second semester.

    • grade_2nd_sem: Average grade in the second semester.

    • academic_status: Academic status of the student.

  3. Socioeconomic Features:

    • mother_qual: Mother’s qualification.

    • father_qual: Father’s qualification.

    • mother_occ: Mother’s occupation.

    • father_occ: Father’s occupation.

    • unemployment_rate: Unemployment rate.

    • inflation_rate: Inflation rate.

    • gdp: GDP.

# Original variable names
original_names <- names(data)

# Define new, shorter names
new_names <- c(
  "marital_status", "app_mode", "app_order", "course", "attendance", 
  "prev_qualification", "prev_grade", "nationality", "mother_qual", 
  "father_qual", "mother_occ", "father_occ", "admission_grade", 
  "displaced", "special_needs", "debtor", "tuition_up_to_date", 
  "gender", "scholarship", "age_enrollment", "international", 
  "credits_1st_sem", "enrolled_1st_sem", "evaluations_1st_sem", 
  "approved_1st_sem", "grade_1st_sem", "no_eval_1st_sem", 
  "credits_2nd_sem", "enrolled_2nd_sem", "evaluations_2nd_sem", 
  "approved_2nd_sem", "grade_2nd_sem", "no_eval_2nd_sem", 
  "unemployment_rate", "inflation_rate", "gdp", "academic_status"
)

# Assign the new names to the data frame
names(data) <- new_names

# Check the updated variable names
names(data)
##  [1] "marital_status"      "app_mode"            "app_order"          
##  [4] "course"              "attendance"          "prev_qualification" 
##  [7] "prev_grade"          "nationality"         "mother_qual"        
## [10] "father_qual"         "mother_occ"          "father_occ"         
## [13] "admission_grade"     "displaced"           "special_needs"      
## [16] "debtor"              "tuition_up_to_date"  "gender"             
## [19] "scholarship"         "age_enrollment"      "international"      
## [22] "credits_1st_sem"     "enrolled_1st_sem"    "evaluations_1st_sem"
## [25] "approved_1st_sem"    "grade_1st_sem"       "no_eval_1st_sem"    
## [28] "credits_2nd_sem"     "enrolled_2nd_sem"    "evaluations_2nd_sem"
## [31] "approved_2nd_sem"    "grade_2nd_sem"       "no_eval_2nd_sem"    
## [34] "unemployment_rate"   "inflation_rate"      "gdp"                
## [37] "academic_status"

First insight into the data

plot_intro(data)

We don’t have missing values, being the vast majority of our columns continuous. However, most of them aren’t in the appropriate format. We first convert categorical variables into factor.

categorical_vars <- c(
  "marital_status", "app_mode", "course", "attendance", 
  "prev_qualification", "nationality", "mother_qual", 
  "father_qual", "mother_occ", "father_occ", 
  "displaced", "special_needs", "debtor", "tuition_up_to_date", 
  "gender", "scholarship", "international", "academic_status")

data[categorical_vars] <- lapply(data[categorical_vars], as.factor)

There were two columns, grade_1st_sem and grade_1st_sem, that caused issues because they contained decimal numbers with multiple periods. In R, such formats are not valid numeric values, causing NA values when attempting to convert them directly to numeric. To fix this, we cleaned the data by extracting only the first decimal point and the following digit, then converted the cleaned strings to numeric values and rounded them to one decimal place. This ensures the data is properly formatted for analysis. However, we also identified and removed records where grades exceeded the maximum possible value of 20, as specified by the dataset creators. This step ensures data integrity and aligns with the established grading scale of 0 to 20.

# Function to clean and round to one decimal place
clean_and_round <- function(column) {
  # Extract the first decimal point and the following digit
  column <- gsub("(\\d+\\.\\d).*", "\\1", column)
  # Convert to numeric and round to one decimal place
  round(as.numeric(column), digits = 1)
}

# Apply the function to the problematic columns
data$grade_1st_sem <- clean_and_round(data$grade_1st_sem)
data$grade_2nd_sem <- clean_and_round(data$grade_2nd_sem)

# Filter records where grade_1st_sem is less than or equal to 20
data <- data[data$grade_1st_sem <= 20, ]
data <- data[data$grade_2nd_sem <= 20, ]

Then, we convert binary variables into numeric.

# List of binary variables
binary_vars <- c("attendance", "displaced", "special_needs", "debtor", 
                 "tuition_up_to_date", "gender", "scholarship", "international")

# Converting binary variables into numeric
data[binary_vars] <- lapply(data[binary_vars], 
                            function(x) as.numeric(as.character(x)))

# Verifying the result
str(data[, binary_vars])
## 'data.frame':    4321 obs. of  8 variables:
##  $ attendance        : num  1 1 1 1 0 0 1 1 1 1 ...
##  $ displaced         : num  1 1 1 1 0 0 1 1 0 1 ...
##  $ special_needs     : num  0 0 0 0 0 0 0 0 0 0 ...
##  $ debtor            : num  0 0 0 0 0 1 0 0 0 1 ...
##  $ tuition_up_to_date: num  1 0 0 1 1 1 1 0 1 0 ...
##  $ gender            : num  1 1 1 0 0 1 0 1 0 0 ...
##  $ scholarship       : num  0 0 0 0 0 0 1 0 1 0 ...
##  $ international     : num  0 0 0 0 0 0 0 0 1 0 ...
# Renaming
colnames(data)[colnames(data) == "gender"] <- "gender_Male" # 1 male 0 female
colnames(data)[colnames(data) == "attendance"] <- "attendance_Daytime"
# 1 daytime 2 evening attendance

Next, we transform factor variables into numeric.

Marital status: we realized the vast majority are single, so we will convert it into a dummy

table(data$marital_status)
## 
##    1    2    3    4    5    6 
## 3824  372    4   90   25    6
data <- data %>%
  mutate(single = ifelse(marital_status == 1, 1, 0)) %>% #If single 1, if not, 0
  dplyr::select(-marital_status)

Application mode: we transform this variable into a set of more specific binary variables, each of them representing a specific and broad category of admission.

table(data$app_mode)
## 
##    1    2    5    7   10   15   16   17   18   26   27   39   42   43   44   51 
## 1666    3   16  137   10   30   38  845  116    1    1  778   73  299  213   59 
##   53   57 
##   35    1
data <- data %>%
  mutate(
    app_regular = ifelse(app_mode %in% c(1, 17, 18), 1, 0),  # Regular Admission
    app_special = ifelse(app_mode %in% c(5, 15, 16, 2, 10, 26, 27), 1, 0),  
    # Special Cases (International, Ordinances, Regional)
    app_over23 = ifelse(app_mode == 39, 1, 0),  # Over 23 Years Old
    app_transfer_coursechange = ifelse(app_mode %in% c(42, 43, 51, 57), 1, 0),  
    # Transfers & Course Changes
    app_previous_highered = ifelse(app_mode %in% c(7, 44, 53), 1, 0)  
    # Holders of Previous Higher Education Degrees
  ) %>%
  dplyr::select(-app_mode)

Course: we do the same for course, grouping them by fields.

table(data$course)
## 
##   33  171 8014 9003 9070 9085 9119 9130 9147 9238 9254 9500 9556 9670 9773 9853 
##   12  215  213  210  226  337  170  140  380  355  252  684   69  268  331  192 
## 9991 
##  267
data <- data %>%
  mutate(
    engineering_tech = ifelse(course %in% c(9119), 1, 0),  
    # Engineering & Technology
    health_sciences = ifelse(course %in% c(9085, 9500, 9556), 1, 0),  
    # Health Sciences
    management_business = ifelse(course %in% c(9147, 9991), 1, 0),  
    # Management & Business
    social_sciences_humanities = ifelse(course %in% c(8014, 9238, 9853), 1, 0),  
    # Social Sciences & Humanities
    agriculture_env = ifelse(course %in% c(33, 9003, 9130), 1, 0),  
    # Agriculture & Environmental Sciences
    arts_media_comm = ifelse(course %in% c(171, 9070, 9670, 9773), 1, 0),  
    # Arts, Media & Communication
    tourism_hospitality = ifelse(course == 9254, 1, 0)  
    # Tourism & Hospitality
  )  %>%
  dplyr::select(-course)

Previous qualification: the vast majority had previous secondary studies so we convert it into a dummy.

table(data$prev_qualification)
## 
##    1    2    3    4    5    6    9   10   12   14   15   19   38   39   40   42 
## 3624   21  124    8    1   16   11    4   45    1    2  159    6  219   38   36 
##   43 
##    6
data <- data %>%
  mutate(secondary_education = ifelse(prev_qualification == 1, 1, 0))%>%
  dplyr::select(-prev_qualification)

Nationality: if Portuguese 1, if not 0

table(data$nationality)
## 
##    1    2    6   11   13   14   17   21   22   24   25   26   32   41   62  100 
## 4212    2   12    3    1    1    1    2   13    5    2   14    1   38    2    3 
##  101  103  105  108  109 
##    2    3    2    1    1
data <- data %>%
  mutate(portuguese = ifelse(nationality == 1, 1, 0))%>%
  dplyr::select(-nationality)

Several studies in educational sociology indicate that maternal education has a stronger influence on student success than paternal education. Empirical evidence from researches such as Davis-Kean (2005) and Fan & Chen (2001) supports this, showing that children of highly educated mothers are more likely to graduate and achieve higher academic performance. Given these findings, variable mother_qual was retained and recategorized, while father_qual and father_occ were removed to limit the number of variables and prioritize the most impactful predictors.

table(data$mother_qual)
## 
##    1    2    3    4    5    6    9   10   11   12   14   18   19   22   26   27 
## 1036   83  426   46   21    4    8    3    3   40    2    1  930    1    1    1 
##   29   30   34   35   36   37   38   39   40   41   42   43   44 
##    3    3  128    3    3  993  550    8    9    6    4    4    1
data <- data %>%
  mutate(
    mother_secondary = ifelse(mother_qual %in% c(1, 9, 10, 12, 14, 18), 1, 0),
    mother_higher = ifelse(mother_qual %in% c(2, 3, 4, 5, 6, 40, 41, 42, 43, 44), 
                           1, 0),
    mother_basic = ifelse(mother_qual %in% c(19, 22, 26, 27, 29, 30, 37, 38, 39), 
                          1, 0),
    mother_illiterate_other = ifelse(mother_qual %in% c(34, 35, 36, 11), 1, 0)
  )%>%
  dplyr::select(-mother_qual, -father_qual, -father_occ)

Mother occupation: we simplified and grouped similar occupations together.

table(data$mother_occ)
## 
##    0    1    2    3    4    5    6    7    8    9   10   90   99  122  123  125 
##  142  102  310  341  787  517   91  265   36 1544    4   70   17    2    7    1 
##  131  132  134  141  143  144  151  152  153  171  173  175  191  192  193  194 
##    1    3    4    8    3    6    3    2    2    1    1    5   26    5    4   11
data <- data %>%
  mutate(
    mother_no_working = ifelse(mother_occ %in% c(0, 90, 99), 1, 0),
    mother_high_position = ifelse(mother_occ %in% c(1, 2, 122, 123, 125), 1, 0),
    mother_technical_admin = ifelse(mother_occ %in% c(3, 131, 132, 134, 141, 143, 
                                                      144), 1, 0),
    mother_services_sales = ifelse(mother_occ %in% c(5, 151, 152, 153, 194), 1, 0),
    mother_agriculture = ifelse(mother_occ %in% c(6, 192), 1, 0),
    mother_industry = ifelse(mother_occ %in% c(7, 8, 171, 173, 175, 193), 1, 0),
    mother_cleaning = ifelse(mother_occ %in% c(191), 1, 0),
    mother_unskilled = ifelse(mother_occ %in% c(9), 1, 0)
  ) %>%
  dplyr::select(-mother_occ)

As we are interested on early prediction, we aim to identify students at risk of dropping out as soon as possible, allowing institutions to implement timely interventions. Unlike models that rely on long-term academic data, our approach emphasizes early university performance. Consequently, we will mantain first-semester information, while excluding second-semester results, ensuring that predictions are made in the initial stages of higher education.

df <- data #starting point for regression

data <- data %>% dplyr::select(-approved_2nd_sem, -enrolled_2nd_sem, 
                               -evaluations_2nd_sem,-grade_2nd_sem, 
                               -credits_2nd_sem, -no_eval_2nd_sem)

Part 1: Classification

Exploratory Data Analysis

Exploring the target variable

prop.table(table(data$academic_status))
## 
##   Dropout  Enrolled  Graduate 
## 0.3267762 0.1821338 0.4910900
# Distribution of academic status
ggplot(data, aes(x = academic_status, fill = academic_status)) +
  geom_bar() +
  labs(title = "Distribution of Academic Status", x = "Academic Status", 
       y = "Count")+
  theme(legend.position = "none")

The dataset shows a slight class imbalance, with Graduates (49.1%) being the most frequent category, followed by Dropouts (32.7%) and Enrolled students (18.2%). Our primary goal is to classify students into all three categories rather than focusing on a binary distinction, since this approach aligns better with the objectives of the course, allowing us to explore multi-class classification challenges. However, we acknowledge that the Enrolled category is the smallest and may be harder for the model to predict accurately. Since our main interest is in identifying students at risk of dropping out, misclassifications in the Dropout category will be considered at the highest cost, while errors in the Enrolled or Graduate categories will be of lesser concern.

Exploring some relations with our target variable:

  1. Academic performance predictors
# Admission Grade vs. Academic Status
ggplot(data, aes(x = academic_status, y = admission_grade, fill = academic_status)) +
  geom_boxplot() +
  labs(title = "Admission Grade Distribution by Academic Status", 
       x = "Academic Status", y = "Admission Grade") +
  theme_minimal()+
  theme(legend.position = "none")

# First Semester Grade vs. Academic Status
ggplot(data, aes(x = academic_status, y = grade_1st_sem, fill = academic_status)) +
  geom_boxplot() +
  labs(title = "First Semester Grade Distribution by Academic Status", 
       x = "Academic Status", y = "First Semester Grade") +
  theme_minimal()+
  theme(legend.position = "none")

# Previous Grade vs. Academic Status
ggplot(data, aes(x = academic_status, y = prev_grade, fill = academic_status)) +
  geom_boxplot() +
  labs(title = "Previous Grade Distribution by Academic Status", 
       x = "Academic Status", y = "Previous Grade") +
  theme_minimal()+
  theme(legend.position = "none")

While previous and admission grades do not seem to show significant differences between the groups, the most striking pattern emerges with the first-semester grades. Graduates tend to have the highest first-semester grades with a compact distribution, while enrolled students have slightly lower but similar medians. In contrast, dropouts exhibit a much wider dispersion, with many students having grades close to zero. This suggests that early academic performance plays a crucial role in determining student outcomes, as those who struggle in their first semester are at a much higher risk of dropping out. The sharp contrast in grade distributions indicates that first-semester performance could serve as a strong early indicator for academic success or failure.

  1. Socioeconomic factors
# Gender vs Academic Status
ggplot(data, aes(x = factor(gender_Male, labels = c("Female", "Male")), 
                 fill = as.factor(academic_status))) +
  geom_bar(position = "fill") + 
  theme_minimal() +
  labs(title = "Gender vs Academic Status", y = "Proportion", 
       x = "Gender", fill = "Academic Status")

# Scholarship vs. Academic Status
ggplot(data, aes(x = factor(scholarship, labels = c("No", "Yes")), 
                 fill = as.factor(academic_status))) +
  geom_bar(position = "fill") +
  labs(title = "Scholarship Holders by Academic Status", 
       x = "Scholarship", y = "Proportion", fill = "Academic Status") +
  theme_minimal()

# Tuition Up-to-Date vs. Academic Status
ggplot(data, aes(x = factor(tuition_up_to_date, labels = c("No", "Yes")), 
                 fill = as.factor(academic_status))) +
  geom_bar(position = "fill") +
  labs(title = "Tuition Payment Status by Academic Status", 
       x = "Tuition up-to-date", y = "Proportion", fill = "Academic Status") +
  theme_minimal()

# Mother's Education vs. Academic Status
ggplot(data, aes(x = factor(mother_secondary, labels = c("No", "Yes")), 
                 fill = as.factor(academic_status))) +
  geom_bar(position = "fill") +
  labs(title = "Mother's Secondary Education & Academic Status", 
       x = "Mother Secondary Educ.", y = "Proportion", fill = "Academic Status") +
  theme_minimal()

Male students tend to dropout more than female and most students who receive a scholarship tend to graduate, while only a small minority of them dropout. On the other hand, among students who do not have a scholarship, the proportions of graduates and dropouts are more balanced.

Additionally, a significant pattern emerges regarding tuition payment status: the majority of students who do not have their tuition up to date appear in the dropout category. Since nearly 80% of students in this situation dropout, this variable might be too dominant and could strongly influence the model. It raises the question of whether we should consider removing it, as it could act more as a direct proxy for dropout rather than an explanatory feature, potentially leading to overly simplistic predictions. We finally decide to remove it.

data <- data %>% dplyr::select(-tuition_up_to_date)
  1. Institutional & enrollment variables
# Application Mode vs. Academic Status
ggplot(data, aes(x = factor(app_regular, labels = c("No", "Yes")), 
                 fill = as.factor(academic_status))) +
  geom_bar(position = "fill") +
  labs(title = "Application Mode & Academic Status", 
       x = "Regular Application", y = "Proportion", fill = "Academic Status") +
  theme_minimal()

# Study Program vs. Academic Status
ggplot(data, aes(x = factor(health_sciences, labels = c("No", "Yes")), 
                 fill = as.factor(academic_status))) +
  geom_bar(position = "fill") +
  labs(title = "Health Sciences Students & Academic Status", 
       x = "Health Sciences", y = "Proportion", fill = "Academic Status") +
  theme_minimal()

People that entered university through the regular modalities are more prone to graduate, compared those who applied by other methods. Moreover, there seems to be a slightly higher proportion of graduates among health sciences students compared to those in other fields of study, maybe due to the vocational nature or compromise these degrees are usually associated with.

Correlation analysis and feature selection

In this section we aim to analyze the correlations between numerical variables in the dataset.

# Select only numeric variables
numeric_data <- data[, sapply(data, is.numeric)]

# Compute the correlation matrix
cor_matrix <- cor(numeric_data, use = "complete.obs") 

# Install and load the corrplot package
library(corrplot)
## corrplot 0.92 loaded
# Plot the correlation matrix
corrplot(cor_matrix, method = "color", type = "upper", tl.col = "black", 
         tl.srt = 45)

The correlation matrix is converted into a data frame to identify highly correlated variable pairs. Pairs with a correlation coefficient above 0.7 (excluding self-correlations) are extracted and sorted by absolute correlation value. This helps detect potential multicollinearity, which may indicate redundant features that should be removed or adjusted to improve model performance.

# Convert the correlation matrix to a data frame
cor_df <- as.data.frame(as.table(cor_matrix))

# Filter pairs with correlation >= 0.8 (excluding self-correlations)
high_cor_pairs <- subset(cor_df, abs(Freq) >= 0.7 & Var1 != Var2)

# Sort by absolute correlation value
high_cor_pairs <- high_cor_pairs[order(-abs(high_cor_pairs$Freq)), ]

# Display the highly correlated pairs
print(high_cor_pairs)
##                  Var1             Var2       Freq
## 505        portuguese    international -1.0000000
## 1609    international       portuguese -1.0000000
## 530  enrolled_1st_sem  credits_1st_sem  0.7762595
## 576   credits_1st_sem enrolled_1st_sem  0.7762595
## 579  approved_1st_sem enrolled_1st_sem  0.7673513
## 671  enrolled_1st_sem approved_1st_sem  0.7673513

We will eliminate “enrolled_1st_sem” and “portuguese” to reduce noise and redundancy in the dataset. “Enrolled_1st_sem” is highly correlated with both “credits_1st_sem” and “approved_1st_sem,” meaning it does not add much independent information. Similarly, “portuguese” and “international” are perfectly negatively correlated, making one of them redundant.

data<-data %>%
  dplyr::select(-portuguese, -enrolled_1st_sem)

Statistical classification

As part of the statistical classification approach, we will explore several models, including multinomial logistic regression, Linear Discriminant Analysis, and Quadratic Discriminant Analysis, which fall under the umbrella of Bayesian- inspired techniques. These models will help us understand the relationships between predictor variables and academic status.

Multinomial logistic regression model

To classify students into Dropout, Enrolled, or Graduate, we begin with a multinomial logistic regression model. This method allows us to model categorical outcomes with more than two classes by estimating the probability of each student belonging to one of the three academic status categories.

First, we split the data into an 80% training set and a 20% testing set to ensure that our model is evaluated on unseen data.

# Data partition 
set.seed(123)  
in_train <- createDataPartition(data$academic_status, p = 0.8, list = FALSE)
training <- data[in_train,]
testing <- data[-in_train,]

nrow(training)
## [1] 3458
nrow(testing)
## [1] 863

We will begin with a theory-driven approach, selecting variables based on domain knowledge and our exploratory data analysis. This will gives us an initial sense of which variables are the most relevant and whether they behave as expected. Additionally, we exponentiate the model coefficients to interpret their effects in terms of odds ratios, helping us understand the impact of different features on the likelihood of a student belonging to each academic category.

# Train the multinomial model with selected predictors
multinom.model <- multinom(academic_status ~ age_enrollment + gender_Male + 
                           scholarship + prev_grade + admission_grade +
                           app_regular + app_over23 + engineering_tech 
                           + health_sciences + social_sciences_humanities
                           + arts_media_comm + unemployment_rate + gdp 
                           + grade_1st_sem + mother_secondary + mother_higher 
                           + mother_basic, 
                           data = training)
## # weights:  57 (36 variable)
## initial  value 3799.001294 
## iter  10 value 3177.076928
## iter  20 value 3036.693240
## iter  30 value 2905.996892
## iter  40 value 2880.282411
## final  value 2880.268210 
## converged
# Display model summary to interpret coefficients
summary(multinom.model)
## Call:
## multinom(formula = academic_status ~ age_enrollment + gender_Male + 
##     scholarship + prev_grade + admission_grade + app_regular + 
##     app_over23 + engineering_tech + health_sciences + social_sciences_humanities + 
##     arts_media_comm + unemployment_rate + gdp + grade_1st_sem + 
##     mother_secondary + mother_higher + mother_basic, data = training)
## 
## Coefficients:
##          (Intercept) age_enrollment gender_Male scholarship    prev_grade
## Enrolled   -2.391291   -0.040412702  -0.2898622    0.486967 -0.0008075199
## Graduate   -5.944324   -0.008016376  -0.4469380    1.379733  0.0036341924
##          admission_grade app_regular app_over23 engineering_tech
## Enrolled     0.001428765 -0.07212635 -0.1717280        0.5485767
## Graduate     0.019440026  0.39605864 -0.5122709       -1.4641001
##          health_sciences social_sciences_humanities arts_media_comm
## Enrolled       0.1804339                 -0.0657495     -0.09346135
## Graduate       0.6840811                  0.4495303      0.40090905
##          unemployment_rate           gdp grade_1st_sem mother_secondary
## Enrolled       -0.08875476 -0.0397340995     0.1264997         2.684212
## Graduate       -0.02375023  0.0002967505     0.1972951         1.293041
##          mother_higher mother_basic
## Enrolled      3.031143     2.624385
## Graduate      1.395557     1.324164
## 
## Std. Errors:
##          (Intercept) age_enrollment gender_Male scholarship  prev_grade
## Enrolled   0.9482232    0.010904433   0.1201398   0.1579744 0.005005757
## Graduate   0.6988920    0.008490139   0.1034572   0.1286428 0.004278093
##          admission_grade app_regular app_over23 engineering_tech
## Enrolled     0.004568172   0.1454873  0.1817738        0.2372268
## Graduate     0.003897892   0.1288979  0.1603113        0.3697414
##          health_sciences social_sciences_humanities arts_media_comm
## Enrolled       0.1531115                  0.1717706       0.1497293
## Graduate       0.1327866                  0.1425631       0.1282734
##          unemployment_rate        gdp grade_1st_sem mother_secondary
## Enrolled        0.02183994 0.02494637    0.01099843        0.6129159
## Graduate        0.01923843 0.02209633    0.01042007        0.3093812
##          mother_higher mother_basic
## Enrolled     0.6194661    0.6055511
## Graduate     0.3226798    0.2970804
## 
## Residual Deviance: 5760.536 
## AIC: 5832.536
# Exponentiate coefficients for better interpretation
exp(coef(multinom.model))
##          (Intercept) age_enrollment gender_Male scholarship prev_grade
## Enrolled 0.091511462      0.9603930   0.7483667    1.627373  0.9991928
## Graduate 0.002620674      0.9920157   0.6395836    3.973842  1.0036408
##          admission_grade app_regular app_over23 engineering_tech
## Enrolled         1.00143   0.9304133  0.8422083         1.730788
## Graduate         1.01963   1.4859565  0.5991335         0.231286
##          health_sciences social_sciences_humanities arts_media_comm
## Enrolled        1.197737                  0.9363654       0.9107732
## Graduate        1.981950                  1.5675758       1.4931815
##          unemployment_rate       gdp grade_1st_sem mother_secondary
## Enrolled         0.9150700 0.9610449      1.134849        14.646656
## Graduate         0.9765296 1.0002968      1.218103         3.643852
##          mother_higher mother_basic
## Enrolled     20.720912    13.796090
## Graduate      4.037222     3.759041

The multinomial model results highlight several key factors influencing student outcomes. Scholarship holders are significantly more likely to graduate or stay enrolled, reinforcing the role of financial support in academic success. Previous and admission grades have a minor but positive effect, while maternal education strongly correlates with higher enrollment and graduation rates. Engineering students are less likely to graduate compared to those in health sciences, potentially reflecting differences in program difficulty. The unemployment rate slightly decreases enrollment likelihood but has minimal impact on graduation.

set.seed(123)
# Predict on the training set
train_preds_multinom <- predict(multinom.model, newdata = training)

# Compute confusion matrix for the training set
conf_matrix_train <- confusionMatrix(train_preds_multinom, 
                                     training$academic_status)
print(conf_matrix_train)
## Confusion Matrix and Statistics
## 
##           Reference
## Prediction Dropout Enrolled Graduate
##   Dropout      685      163      210
##   Enrolled      28       43       17
##   Graduate     417      424     1471
## 
## Overall Statistics
##                                          
##                Accuracy : 0.6359         
##                  95% CI : (0.6196, 0.652)
##     No Information Rate : 0.491          
##     P-Value [Acc > NIR] : < 2.2e-16      
##                                          
##                   Kappa : 0.358          
##                                          
##  Mcnemar's Test P-Value : < 2.2e-16      
## 
## Statistics by Class:
## 
##                      Class: Dropout Class: Enrolled Class: Graduate
## Sensitivity                  0.6062         0.06825          0.8663
## Specificity                  0.8398         0.98409          0.5222
## Pos Pred Value               0.6474         0.48864          0.6362
## Neg Pred Value               0.8146         0.82582          0.8019
## Prevalence                   0.3268         0.18219          0.4910
## Detection Rate               0.1981         0.01243          0.4254
## Detection Prevalence         0.3060         0.02545          0.6686
## Balanced Accuracy            0.7230         0.52617          0.6942

The confusion matrix shows an overall accuracy of 63.6%, performing well for predicting graduates (86.6% sensitivity) and moderately for dropouts (60.6%). However, it struggles with enrolled students (6.8% sensitivity), likely due to class imbalance.

# Predict on the test set
test_preds_multinom <- predict(multinom.model, newdata = testing)

# Compute confusion matrix for the test set
conf_matrix_test <- confusionMatrix(test_preds_multinom, testing$academic_status)
print(conf_matrix_test)
## Confusion Matrix and Statistics
## 
##           Reference
## Prediction Dropout Enrolled Graduate
##   Dropout      176       45       55
##   Enrolled      13        7        5
##   Graduate      93      105      364
## 
## Overall Statistics
##                                           
##                Accuracy : 0.6338          
##                  95% CI : (0.6007, 0.6661)
##     No Information Rate : 0.4913          
##     P-Value [Acc > NIR] : < 2.2e-16       
##                                           
##                   Kappa : 0.3579          
##                                           
##  Mcnemar's Test P-Value : < 2.2e-16       
## 
## Statistics by Class:
## 
##                      Class: Dropout Class: Enrolled Class: Graduate
## Sensitivity                  0.6241        0.044586          0.8585
## Specificity                  0.8279        0.974504          0.5490
## Pos Pred Value               0.6377        0.280000          0.6477
## Neg Pred Value               0.8194        0.821002          0.8007
## Prevalence                   0.3268        0.181924          0.4913
## Detection Rate               0.2039        0.008111          0.4218
## Detection Prevalence         0.3198        0.028969          0.6512
## Balanced Accuracy            0.7260        0.509545          0.7037

Overall, the model is performing well for dropout and graduate predictions but has difficulty identifying enrolled students due probably to class imbalance and underrepresentation.

We are now going to visualize two graphs useful for understanding how predictor variables impact the likelihood of a student being classified into the different academic statuses, allowing us to interpret the model’s behavior more intuitively.

# Visualizar el impacto de una variable
gg.pred <- ggpredict(multinom.model, terms = "mother_secondary")
plot(gg.pred)

# Visualizar el impacto de una variable
gg.pred <- ggpredict(multinom.model, terms = "grade_1st_sem")
## Data were 'prettified'. Consider using `terms="grade_1st_sem [all]"` to
##   get smooth plots.
plot(gg.pred)

The first graph suggests that having a mother with secondary education positively influences a student’s chances of continuing their education and graduating, aligning with findings from sociological studies on parental education. The second one highlights how first semester grade plays a key role in predicting a student’s academic status, with lower grades correlating with higher dropout probabilities, and higher grades correlating with higher graduation probabilities.

Lasso regularized multinomial model

set.seed(123)

# Preparing data for glmnet
y_train <- as.numeric(training$academic_status) - 1  
y_test <- as.numeric(testing$academic_status) - 1  

# Matrix creation 
X_train <- model.matrix(academic_status ~ ., data = training)[,-1]
X_test <- model.matrix(academic_status ~ ., data = testing)[,-1]

We train the model

set.seed(123)

# Train Lasso model
lasso_model <- cv.glmnet(X_train, y_train, 
                         family = "multinomial", 
                         alpha = 1,  # (L1 penalization)
                         type.multinomial = "grouped")

# Select best lambda
best_lambda <- lasso_model$lambda.min
print(best_lambda)
## [1] 0.004189825

We make predictions on the training set

lasso_preds <- predict(lasso_model, newx = X_test, s = "lambda.min", 
                       type = "response")

# We select the highest probablity class
lasso_preds <- apply(lasso_preds, 1, which.max) - 1  

# Converting to factor
lasso_preds <- as.factor(lasso_preds + 1)
y_test_factor <- as.factor(y_test + 1)

# Evalutation
conf_matrix_lasso <- confusionMatrix(lasso_preds, y_test_factor)
print(conf_matrix_lasso)
## Confusion Matrix and Statistics
## 
##           Reference
## Prediction   1   2   3
##          1 224  52  37
##          2  19  25  13
##          3  39  80 374
## 
## Overall Statistics
##                                           
##                Accuracy : 0.7219          
##                  95% CI : (0.6907, 0.7516)
##     No Information Rate : 0.4913          
##     P-Value [Acc > NIR] : < 2.2e-16       
##                                           
##                   Kappa : 0.5277          
##                                           
##  Mcnemar's Test P-Value : 9.706e-14       
## 
## Statistics by Class:
## 
##                      Class: 1 Class: 2 Class: 3
## Sensitivity            0.7943  0.15924   0.8821
## Specificity            0.8468  0.95467   0.7289
## Pos Pred Value         0.7157  0.43860   0.7586
## Neg Pred Value         0.8945  0.83623   0.8649
## Prevalence             0.3268  0.18192   0.4913
## Detection Rate         0.2596  0.02897   0.4334
## Detection Prevalence   0.3627  0.06605   0.5713
## Balanced Accuracy      0.8206  0.55695   0.8055

The confusion matrix results show that the model has an overall accuracy of 72.07%, with a Kappa value of 0.5256, indicating moderate agreement between predicted and actual values. The model performs better at predicting Dropout (Class 1) and Graduate (Class 3) statuses, with accuracy rates of 79.43% and 88.21% respectively, while the model struggles more with predicting the Enrolled (Class 2) status, with only 15.29% sensitivity.

# Extract coefficients
lasso_coefs <- coef(lasso_model, s = "lambda.min")
print(lasso_coefs)
## $`0`
## 46 x 1 sparse Matrix of class "dgCMatrix"
##                                       1
## (Intercept)                 0.713237499
## app_order                   0.074965630
## attendance_Daytime          0.081770616
## prev_grade                  .          
## admission_grade            -0.005367366
## displaced                   0.001255805
## special_needs               .          
## debtor                      0.803788614
## gender_Male                 0.192317793
## scholarship                -0.485826131
## age_enrollment              0.021278702
## international               .          
## credits_1st_sem             0.244667222
## evaluations_1st_sem         0.033408020
## approved_1st_sem           -0.381287686
## grade_1st_sem              -0.003900635
## no_eval_1st_sem            -0.021975143
## unemployment_rate           0.044492577
## inflation_rate              0.004378908
## gdp                         0.004117625
## single                      0.027663899
## app_regular                 0.008724782
## app_special                -0.392875174
## app_over23                  0.160284497
## app_transfer_coursechange   .          
## app_previous_highered      -0.015669453
## engineering_tech           -0.050259634
## health_sciences             .          
## management_business        -0.086659816
## social_sciences_humanities  0.024904787
## agriculture_env             0.088471695
## arts_media_comm            -0.044605126
## tourism_hospitality         0.329524457
## secondary_education        -0.085815503
## mother_secondary            .          
## mother_higher              -0.134894895
## mother_basic                0.009704527
## mother_illiterate_other     0.619934215
## mother_no_working           0.654605697
## mother_high_position        .          
## mother_technical_admin     -0.012273604
## mother_services_sales       0.045981131
## mother_agriculture         -0.227116850
## mother_industry             0.004761837
## mother_cleaning            -2.044171816
## mother_unskilled           -0.045483148
## 
## $`1`
## 46 x 1 sparse Matrix of class "dgCMatrix"
##                                        1
## (Intercept)                 0.5804972035
## app_order                  -0.0608636633
## attendance_Daytime          0.0014453782
## prev_grade                  .           
## admission_grade            -0.0030127380
## displaced                  -0.0006902969
## special_needs               .           
## debtor                      0.0595532251
## gender_Male                -0.0258818504
## scholarship                -0.1012044168
## age_enrollment             -0.0140366944
## international               .           
## credits_1st_sem            -0.0884042928
## evaluations_1st_sem         0.0894775719
## approved_1st_sem           -0.0688167494
## grade_1st_sem               0.0041652024
## no_eval_1st_sem            -0.0142062241
## unemployment_rate          -0.0445904518
## inflation_rate              0.0070865919
## gdp                         0.0010018119
## single                     -0.0354694685
## app_regular                -0.1122477080
## app_special                 0.2288139878
## app_over23                 -0.0886461914
## app_transfer_coursechange   .           
## app_previous_highered       0.0225367201
## engineering_tech            0.7836092224
## health_sciences             .           
## management_business         0.1969500845
## social_sciences_humanities -0.0747001882
## agriculture_env            -0.1582565682
## arts_media_comm             0.0134068565
## tourism_hospitality        -0.2106812790
## secondary_education         0.2118050807
## mother_secondary            .           
## mother_higher               0.1752861196
## mother_basic               -0.0141760523
## mother_illiterate_other    -0.3262784999
## mother_no_working          -1.2158892278
## mother_high_position        .           
## mother_technical_admin      0.0607512666
## mother_services_sales       0.0168180650
## mother_agriculture          0.0009180042
## mother_industry             0.0248528326
## mother_cleaning             1.0822797216
## mother_unskilled           -0.0316269807
## 
## $`2`
## 46 x 1 sparse Matrix of class "dgCMatrix"
##                                        1
## (Intercept)                -1.293735e+00
## app_order                  -1.410197e-02
## attendance_Daytime         -8.321599e-02
## prev_grade                  .           
## admission_grade             8.380104e-03
## displaced                  -5.655081e-04
## special_needs               .           
## debtor                     -8.633418e-01
## gender_Male                -1.664359e-01
## scholarship                 5.870305e-01
## age_enrollment             -7.242008e-03
## international               .           
## credits_1st_sem            -1.562629e-01
## evaluations_1st_sem        -1.228856e-01
## approved_1st_sem            4.501044e-01
## grade_1st_sem              -2.645671e-04
## no_eval_1st_sem             3.618137e-02
## unemployment_rate           9.787526e-05
## inflation_rate             -1.146550e-02
## gdp                        -5.119437e-03
## single                      7.805570e-03
## app_regular                 1.035229e-01
## app_special                 1.640612e-01
## app_over23                 -7.163831e-02
## app_transfer_coursechange   .           
## app_previous_highered      -6.867267e-03
## engineering_tech           -7.333496e-01
## health_sciences             .           
## management_business        -1.102903e-01
## social_sciences_humanities  4.979540e-02
## agriculture_env             6.978487e-02
## arts_media_comm             3.119827e-02
## tourism_hospitality        -1.188432e-01
## secondary_education        -1.259896e-01
## mother_secondary            .           
## mother_higher              -4.039122e-02
## mother_basic                4.471526e-03
## mother_illiterate_other    -2.936557e-01
## mother_no_working           5.612835e-01
## mother_high_position        .           
## mother_technical_admin     -4.847766e-02
## mother_services_sales      -6.279920e-02
## mother_agriculture          2.261988e-01
## mother_industry            -2.961467e-02
## mother_cleaning             9.618921e-01
## mother_unskilled            7.711013e-02

Financial aspects play a crucial role, with debtor status increasing dropout likelihood, while scholarships significantly enhance graduation prospects. Maternal education emerges as a powerful predictor across all outcomes, with higher levels generally associated with better student performance. The type of application (regular vs. special) shows some impact on enrollment status. Interestingly, maternal employment status also influences graduation rates, with students whose mothers are not working or are in cleaning occupations showing higher graduation probabilities.

Making predictions on the testing set

# Make predictions on the testing set
lasso_preds_test <- predict(lasso_model, newx = X_test, s = "lambda.min", 
                            type = "response")

# Since glmnet returns probabilities, we select the class with the highest probability
lasso_preds_test <- apply(lasso_preds_test, 1, which.max) - 1  

# Convert the predictions and the test labels to factors for confusion matrix comparison
lasso_preds_test <- as.factor(lasso_preds_test + 1)
y_test_factor <- as.factor(y_test + 1)

# Evaluate the model performance with confusion matrix
conf_matrix_lasso_test <- confusionMatrix(lasso_preds_test, y_test_factor)

# Print confusion matrix
print(conf_matrix_lasso_test)
## Confusion Matrix and Statistics
## 
##           Reference
## Prediction   1   2   3
##          1 224  52  37
##          2  19  25  13
##          3  39  80 374
## 
## Overall Statistics
##                                           
##                Accuracy : 0.7219          
##                  95% CI : (0.6907, 0.7516)
##     No Information Rate : 0.4913          
##     P-Value [Acc > NIR] : < 2.2e-16       
##                                           
##                   Kappa : 0.5277          
##                                           
##  Mcnemar's Test P-Value : 9.706e-14       
## 
## Statistics by Class:
## 
##                      Class: 1 Class: 2 Class: 3
## Sensitivity            0.7943  0.15924   0.8821
## Specificity            0.8468  0.95467   0.7289
## Pos Pred Value         0.7157  0.43860   0.7586
## Neg Pred Value         0.8945  0.83623   0.8649
## Prevalence             0.3268  0.18192   0.4913
## Detection Rate         0.2596  0.02897   0.4334
## Detection Prevalence   0.3627  0.06605   0.5713
## Balanced Accuracy      0.8206  0.55695   0.8055

We see how accuracy is better than in the previous one (72.07%) and sensitivity for the dropout class is better too (79.43%).

# Extracting number of selected variables
lasso_coefs_matrix <- as.matrix(lasso_coefs[[3]])
non_zero_coefs <- sum(lasso_coefs_matrix != 0)
print(non_zero_coefs)
## [1] 39

We realize lasso performs better but uses too many variables. Taking advantage of its information, we will create a new multinomial logistic regression model, just using 13 variables.

Seccond attempt multinomial logistic regression model

set.seed(123) 
in_train <- createDataPartition(data$academic_status, p = 0.8, list = FALSE)
training <- data[in_train,]
testing <- data[-in_train,]

# Train the new multinomial model with selected predictors
multinom.model2 <- multinom(academic_status ~ mother_cleaning + debtor +
                              mother_no_working +mother_illiterate_other + 
                              tourism_hospitality +credits_1st_sem +gender_Male +
                              app_over23 +mother_higher + mother_agriculture + 
                              approved_1st_sem +app_special +scholarship,
                            data = training)
## # weights:  45 (28 variable)
## initial  value 3799.001294 
## iter  10 value 2847.169808
## iter  20 value 2531.643284
## iter  30 value 2499.446402
## iter  40 value 2497.830449
## iter  50 value 2497.757810
## final  value 2497.757708 
## converged
# Predict on the training set
train_preds_multinom2 <- predict(multinom.model2, newdata = training)

# Compute confusion matrix for the training set
conf_matrix_train2 <- confusionMatrix(train_preds_multinom2, 
                                      training$academic_status)
print(conf_matrix_train2)
## Confusion Matrix and Statistics
## 
##           Reference
## Prediction Dropout Enrolled Graduate
##   Dropout      868      232      125
##   Enrolled      10       26       10
##   Graduate     252      372     1563
## 
## Overall Statistics
##                                           
##                Accuracy : 0.7105          
##                  95% CI : (0.6951, 0.7256)
##     No Information Rate : 0.491           
##     P-Value [Acc > NIR] : < 2.2e-16       
##                                           
##                   Kappa : 0.4933          
##                                           
##  Mcnemar's Test P-Value : < 2.2e-16       
## 
## Statistics by Class:
## 
##                      Class: Dropout Class: Enrolled Class: Graduate
## Sensitivity                  0.7681        0.041270          0.9205
## Specificity                  0.8466        0.992928          0.6455
## Pos Pred Value               0.7086        0.565217          0.7147
## Neg Pred Value               0.8827        0.822978          0.8938
## Prevalence                   0.3268        0.182186          0.4910
## Detection Rate               0.2510        0.007519          0.4520
## Detection Prevalence         0.3543        0.013302          0.6324
## Balanced Accuracy            0.8074        0.517099          0.7830
# Predict on the test set
test_preds_multinom2 <- predict(multinom.model2, newdata = testing)

# Compute confusion matrix for the test set
conf_matrix_test2 <- confusionMatrix(test_preds_multinom2, 
                                     testing$academic_status)
print(conf_matrix_test2)
## Confusion Matrix and Statistics
## 
##           Reference
## Prediction Dropout Enrolled Graduate
##   Dropout      224       61       42
##   Enrolled       2        3        1
##   Graduate      56       93      381
## 
## Overall Statistics
##                                           
##                Accuracy : 0.7045          
##                  95% CI : (0.6728, 0.7348)
##     No Information Rate : 0.4913          
##     P-Value [Acc > NIR] : < 2.2e-16       
##                                           
##                   Kappa : 0.4845          
##                                           
##  Mcnemar's Test P-Value : < 2.2e-16       
## 
## Statistics by Class:
## 
##                      Class: Dropout Class: Enrolled Class: Graduate
## Sensitivity                  0.7943        0.019108          0.8986
## Specificity                  0.8227        0.995751          0.6606
## Pos Pred Value               0.6850        0.500000          0.7189
## Neg Pred Value               0.8918        0.820303          0.8709
## Prevalence                   0.3268        0.181924          0.4913
## Detection Rate               0.2596        0.003476          0.4415
## Detection Prevalence         0.3789        0.006952          0.6141
## Balanced Accuracy            0.8085        0.507429          0.7796

These results show the performance of the multinomial model on both the training and testing sets. We see a 70.45% overall accuracy in the testing set, and 79.43% sensitivity and 82.27% specificity for the dropout category. We prefer this last model due to its simplicity and interpretability with a comparable performance.

Linear Discriminant Analysis (LDA)

Now, we will apply LDA to predict the academic status of students. We will use the selected variables based on previous analysis and the results from our prior models to train the LDA model.

set.seed(123)
lda_model <- lda(academic_status ~ mother_cleaning+debtor +mother_no_working + 
                   mother_illiterate_other + tourism_hospitality +credits_1st_sem 
                 +gender_Male +app_over23 +mother_higher + mother_agriculture + 
                   approved_1st_sem +app_special +scholarship, 
                 data = training)

# Predictions in the testing set
lda_preds <- predict(lda_model, newdata = testing)

# Model evaluation
conf_matrix_lda <- confusionMatrix(lda_preds$class, testing$academic_status)
print(conf_matrix_lda)
## Confusion Matrix and Statistics
## 
##           Reference
## Prediction Dropout Enrolled Graduate
##   Dropout      221       53       41
##   Enrolled       2        4        2
##   Graduate      59      100      381
## 
## Overall Statistics
##                                           
##                Accuracy : 0.7022          
##                  95% CI : (0.6705, 0.7326)
##     No Information Rate : 0.4913          
##     P-Value [Acc > NIR] : < 2.2e-16       
##                                           
##                   Kappa : 0.479           
##                                           
##  Mcnemar's Test P-Value : < 2.2e-16       
## 
## Statistics by Class:
## 
##                      Class: Dropout Class: Enrolled Class: Graduate
## Sensitivity                  0.7837        0.025478          0.8986
## Specificity                  0.8382        0.994334          0.6378
## Pos Pred Value               0.7016        0.500000          0.7056
## Neg Pred Value               0.8887        0.821053          0.8669
## Prevalence                   0.3268        0.181924          0.4913
## Detection Rate               0.2561        0.004635          0.4415
## Detection Prevalence         0.3650        0.009270          0.6257
## Balanced Accuracy            0.8109        0.509906          0.7682

The LDA model performs a bit worse compared to our last model, with an overall accuracy of 70.22% (vs 70.45%). Regarding its performance related to the dropout category, it has a slightly better specificity (83.82% vs 82.27%), but the most important metric in this case is sensitivity in which it performs a bit worse (78.37% vs 79.43%). Our multinom.model2 is the best one up to the moment.

Quadratic Discriminant Analysis (QDA)

Next, we will implement and evaluate QDA model.

# Train QDA model
qda_model <- qda(academic_status~ debtor +mother_no_working +tourism_hospitality 
                 +credits_1st_sem +gender_Male +app_over23 +mother_higher
                 +mother_agriculture +approved_1st_sem +app_special +scholarship, 
                 data = training)

#  Predictions in the testing set
prediction_qda <- predict(qda_model, newdata = testing)$class

# Evaluation
conf_matrix_qda <- confusionMatrix(prediction_qda, testing$academic_status)
print(conf_matrix_qda)
## Confusion Matrix and Statistics
## 
##           Reference
## Prediction Dropout Enrolled Graduate
##   Dropout      177       32       35
##   Enrolled      74       70      107
##   Graduate      31       55      282
## 
## Overall Statistics
##                                           
##                Accuracy : 0.613           
##                  95% CI : (0.5796, 0.6456)
##     No Information Rate : 0.4913          
##     P-Value [Acc > NIR] : 4.656e-13       
##                                           
##                   Kappa : 0.4001          
##                                           
##  Mcnemar's Test P-Value : 2.435e-07       
## 
## Statistics by Class:
## 
##                      Class: Dropout Class: Enrolled Class: Graduate
## Sensitivity                  0.6277         0.44586          0.6651
## Specificity                  0.8847         0.74363          0.8041
## Pos Pred Value               0.7254         0.27888          0.7663
## Neg Pred Value               0.8304         0.85784          0.7131
## Prevalence                   0.3268         0.18192          0.4913
## Detection Rate               0.2051         0.08111          0.3268
## Detection Prevalence         0.2827         0.29085          0.4264
## Balanced Accuracy            0.7562         0.59474          0.7346

The QDA model performed worse than the previous models in terms of overall accuracy (61.3%) and predict worse in every metric.

Machine Learning

After evaluating these statistical models, we will transition to machine learning techniques to improve prediction accuracy and further refine our understanding of the data.

# Configure control for 10-fold cross validation
ctrl <- trainControl(
  method = "repeatedcv", 
  number = 10,
  repeats = 3,  
  classProbs = TRUE,  
  summaryFunction = multiClassSummary, 
  verboseIter = TRUE
)

Benchmark model

Our first move will be establishing a Benchmark model. This model predicts the most frequent class, in this case, Graduate, without considering any predictor variables. It serves as a baseline to compare the performance of more advanced models.

# Benchmark: Regla de Mayoría (predice siempre Graduate)
majority_class <- names(which.max(table(training$academic_status)))
benchmark_preds <- factor(rep(majority_class, nrow(testing)), 
                          levels = levels(testing$academic_status))

# Evaluar Benchmark
conf_matrix_benchmark <- confusionMatrix(benchmark_preds, testing$academic_status)

# Imprimir resultados
print(conf_matrix_benchmark)
## Confusion Matrix and Statistics
## 
##           Reference
## Prediction Dropout Enrolled Graduate
##   Dropout        0        0        0
##   Enrolled       0        0        0
##   Graduate     282      157      424
## 
## Overall Statistics
##                                           
##                Accuracy : 0.4913          
##                  95% CI : (0.4575, 0.5252)
##     No Information Rate : 0.4913          
##     P-Value [Acc > NIR] : 0.5135          
##                                           
##                   Kappa : 0               
##                                           
##  Mcnemar's Test P-Value : NA              
## 
## Statistics by Class:
## 
##                      Class: Dropout Class: Enrolled Class: Graduate
## Sensitivity                  0.0000          0.0000          1.0000
## Specificity                  1.0000          1.0000          0.0000
## Pos Pred Value                  NaN             NaN          0.4913
## Neg Pred Value               0.6732          0.8181             NaN
## Prevalence                   0.3268          0.1819          0.4913
## Detection Rate               0.0000          0.0000          0.4913
## Detection Prevalence         0.0000          0.0000          1.0000
## Balanced Accuracy            0.5000          0.5000          0.5000

The overall accuracy of the model is 49.94%. This benchmark serves as a minimum reference point: any model we build must exceed it.

k-Nearest Neighbors (k-NN)

Now, we will explore the k-NN algorithm.

set.seed(123)

knnFit <- train(
  academic_status ~ ., 
  data = training,
  method = "kknn",   
  preProc = c('scale', 'center'),
  tuneLength = 5, 
  metric = "Accuracy",
  trControl = ctrl
)
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## + Fold01.Rep3: kmax=13, distance=2, kernel=optimal 
## - Fold01.Rep3: kmax=13, distance=2, kernel=optimal 
## + Fold02.Rep3: kmax= 5, distance=2, kernel=optimal 
## - Fold02.Rep3: kmax= 5, distance=2, kernel=optimal 
## + Fold02.Rep3: kmax= 7, distance=2, kernel=optimal 
## - Fold02.Rep3: kmax= 7, distance=2, kernel=optimal 
## + Fold02.Rep3: kmax= 9, distance=2, kernel=optimal 
## - Fold02.Rep3: kmax= 9, distance=2, kernel=optimal 
## + Fold02.Rep3: kmax=11, distance=2, kernel=optimal 
## - Fold02.Rep3: kmax=11, distance=2, kernel=optimal 
## + Fold02.Rep3: kmax=13, distance=2, kernel=optimal 
## - Fold02.Rep3: kmax=13, distance=2, kernel=optimal 
## + Fold03.Rep3: kmax= 5, distance=2, kernel=optimal 
## - Fold03.Rep3: kmax= 5, distance=2, kernel=optimal 
## + Fold03.Rep3: kmax= 7, distance=2, kernel=optimal 
## - Fold03.Rep3: kmax= 7, distance=2, kernel=optimal 
## + Fold03.Rep3: kmax= 9, distance=2, kernel=optimal 
## - Fold03.Rep3: kmax= 9, distance=2, kernel=optimal 
## + Fold03.Rep3: kmax=11, distance=2, kernel=optimal 
## - Fold03.Rep3: kmax=11, distance=2, kernel=optimal 
## + Fold03.Rep3: kmax=13, distance=2, kernel=optimal 
## - Fold03.Rep3: kmax=13, distance=2, kernel=optimal 
## + Fold04.Rep3: kmax= 5, distance=2, kernel=optimal 
## - Fold04.Rep3: kmax= 5, distance=2, kernel=optimal 
## + Fold04.Rep3: kmax= 7, distance=2, kernel=optimal 
## - Fold04.Rep3: kmax= 7, distance=2, kernel=optimal 
## + Fold04.Rep3: kmax= 9, distance=2, kernel=optimal 
## - Fold04.Rep3: kmax= 9, distance=2, kernel=optimal 
## + Fold04.Rep3: kmax=11, distance=2, kernel=optimal 
## - Fold04.Rep3: kmax=11, distance=2, kernel=optimal 
## + Fold04.Rep3: kmax=13, distance=2, kernel=optimal 
## - Fold04.Rep3: kmax=13, distance=2, kernel=optimal 
## + Fold05.Rep3: kmax= 5, distance=2, kernel=optimal 
## - Fold05.Rep3: kmax= 5, distance=2, kernel=optimal 
## + Fold05.Rep3: kmax= 7, distance=2, kernel=optimal 
## - Fold05.Rep3: kmax= 7, distance=2, kernel=optimal 
## + Fold05.Rep3: kmax= 9, distance=2, kernel=optimal 
## - Fold05.Rep3: kmax= 9, distance=2, kernel=optimal 
## + Fold05.Rep3: kmax=11, distance=2, kernel=optimal 
## - Fold05.Rep3: kmax=11, distance=2, kernel=optimal 
## + Fold05.Rep3: kmax=13, distance=2, kernel=optimal 
## - Fold05.Rep3: kmax=13, distance=2, kernel=optimal 
## + Fold06.Rep3: kmax= 5, distance=2, kernel=optimal 
## - Fold06.Rep3: kmax= 5, distance=2, kernel=optimal 
## + Fold06.Rep3: kmax= 7, distance=2, kernel=optimal 
## - Fold06.Rep3: kmax= 7, distance=2, kernel=optimal 
## + Fold06.Rep3: kmax= 9, distance=2, kernel=optimal 
## - Fold06.Rep3: kmax= 9, distance=2, kernel=optimal 
## + Fold06.Rep3: kmax=11, distance=2, kernel=optimal 
## - Fold06.Rep3: kmax=11, distance=2, kernel=optimal 
## + Fold06.Rep3: kmax=13, distance=2, kernel=optimal 
## - Fold06.Rep3: kmax=13, distance=2, kernel=optimal 
## + Fold07.Rep3: kmax= 5, distance=2, kernel=optimal 
## - Fold07.Rep3: kmax= 5, distance=2, kernel=optimal 
## + Fold07.Rep3: kmax= 7, distance=2, kernel=optimal 
## - Fold07.Rep3: kmax= 7, distance=2, kernel=optimal 
## + Fold07.Rep3: kmax= 9, distance=2, kernel=optimal 
## - Fold07.Rep3: kmax= 9, distance=2, kernel=optimal 
## + Fold07.Rep3: kmax=11, distance=2, kernel=optimal 
## - Fold07.Rep3: kmax=11, distance=2, kernel=optimal 
## + Fold07.Rep3: kmax=13, distance=2, kernel=optimal 
## - Fold07.Rep3: kmax=13, distance=2, kernel=optimal 
## + Fold08.Rep3: kmax= 5, distance=2, kernel=optimal 
## - Fold08.Rep3: kmax= 5, distance=2, kernel=optimal 
## + Fold08.Rep3: kmax= 7, distance=2, kernel=optimal 
## - Fold08.Rep3: kmax= 7, distance=2, kernel=optimal 
## + Fold08.Rep3: kmax= 9, distance=2, kernel=optimal 
## - Fold08.Rep3: kmax= 9, distance=2, kernel=optimal 
## + Fold08.Rep3: kmax=11, distance=2, kernel=optimal 
## - Fold08.Rep3: kmax=11, distance=2, kernel=optimal 
## + Fold08.Rep3: kmax=13, distance=2, kernel=optimal 
## - Fold08.Rep3: kmax=13, distance=2, kernel=optimal 
## + Fold09.Rep3: kmax= 5, distance=2, kernel=optimal 
## - Fold09.Rep3: kmax= 5, distance=2, kernel=optimal 
## + Fold09.Rep3: kmax= 7, distance=2, kernel=optimal 
## - Fold09.Rep3: kmax= 7, distance=2, kernel=optimal 
## + Fold09.Rep3: kmax= 9, distance=2, kernel=optimal 
## - Fold09.Rep3: kmax= 9, distance=2, kernel=optimal 
## + Fold09.Rep3: kmax=11, distance=2, kernel=optimal 
## - Fold09.Rep3: kmax=11, distance=2, kernel=optimal 
## + Fold09.Rep3: kmax=13, distance=2, kernel=optimal 
## - Fold09.Rep3: kmax=13, distance=2, kernel=optimal 
## + Fold10.Rep3: kmax= 5, distance=2, kernel=optimal 
## - Fold10.Rep3: kmax= 5, distance=2, kernel=optimal 
## + Fold10.Rep3: kmax= 7, distance=2, kernel=optimal 
## - Fold10.Rep3: kmax= 7, distance=2, kernel=optimal 
## + Fold10.Rep3: kmax= 9, distance=2, kernel=optimal 
## - Fold10.Rep3: kmax= 9, distance=2, kernel=optimal 
## + Fold10.Rep3: kmax=11, distance=2, kernel=optimal 
## - Fold10.Rep3: kmax=11, distance=2, kernel=optimal 
## + Fold10.Rep3: kmax=13, distance=2, kernel=optimal 
## - Fold10.Rep3: kmax=13, distance=2, kernel=optimal 
## Aggregating results
## Selecting tuning parameters
## Fitting kmax = 13, distance = 2, kernel = optimal on full training set
# Predictions
knnProb <- predict(knnFit, testing, type="prob")
prediction_knn <- predict(knnFit, testing)

# Evaluation
conf_matrix_knn <- confusionMatrix(prediction_knn, testing$academic_status)
print(conf_matrix_knn)
## Confusion Matrix and Statistics
## 
##           Reference
## Prediction Dropout Enrolled Graduate
##   Dropout      163       33       41
##   Enrolled      41       35       31
##   Graduate      78       89      352
## 
## Overall Statistics
##                                           
##                Accuracy : 0.6373          
##                  95% CI : (0.6042, 0.6695)
##     No Information Rate : 0.4913          
##     P-Value [Acc > NIR] : < 2.2e-16       
##                                           
##                   Kappa : 0.3876          
##                                           
##  Mcnemar's Test P-Value : 8.755e-09       
## 
## Statistics by Class:
## 
##                      Class: Dropout Class: Enrolled Class: Graduate
## Sensitivity                  0.5780         0.22293          0.8302
## Specificity                  0.8726         0.89802          0.6196
## Pos Pred Value               0.6878         0.32710          0.6782
## Neg Pred Value               0.8099         0.83862          0.7907
## Prevalence                   0.3268         0.18192          0.4913
## Detection Rate               0.1889         0.04056          0.4079
## Detection Prevalence         0.2746         0.12399          0.6014
## Balanced Accuracy            0.7253         0.56047          0.7249

In the results, the k-NN model shows an accuracy of 63.73%, which is better than the benchmark model, but still worse than our last multinomial.

Decision tree

Next, let’s see if the Decision Tree algorithm works better for our dataset.

set.seed(123)
# Train the Decision Tree
control <- rpart.control(minsplit = 8, maxdepth = 12, cp=0.001)
dtFit <- rpart(academic_status ~ ., data = training, method = "class", 
               control = control)

# Visualization
rpart.plot(dtFit, digits = 3)
## Warning: labs do not fit even at cex 0.15, there may be some overplotting

# Prediction
dtPred <- predict(dtFit, testing, type = "class")

# Evaluation
conf_matrix_dt <- confusionMatrix(dtPred, testing$academic_status)
print(conf_matrix_dt)
## Confusion Matrix and Statistics
## 
##           Reference
## Prediction Dropout Enrolled Graduate
##   Dropout      194       44       39
##   Enrolled      40       38       36
##   Graduate      48       75      349
## 
## Overall Statistics
##                                           
##                Accuracy : 0.6732          
##                  95% CI : (0.6408, 0.7045)
##     No Information Rate : 0.4913          
##     P-Value [Acc > NIR] : < 2.2e-16       
##                                           
##                   Kappa : 0.4575          
##                                           
##  Mcnemar's Test P-Value : 0.001973        
## 
## Statistics by Class:
## 
##                      Class: Dropout Class: Enrolled Class: Graduate
## Sensitivity                  0.6879         0.24204          0.8231
## Specificity                  0.8571         0.89235          0.7198
## Pos Pred Value               0.7004         0.33333          0.7394
## Neg Pred Value               0.8498         0.84112          0.8082
## Prevalence                   0.3268         0.18192          0.4913
## Detection Rate               0.2248         0.04403          0.4044
## Detection Prevalence         0.3210         0.13210          0.5469
## Balanced Accuracy            0.7725         0.56719          0.7715

In the results, the Decision Tree model shows an accuracy of 67.32%, which is better than the k-NN model but still not better than out winner up to the moment.

Random forest

Now we will try with the Random Forest (RF) model but we will try to reduce its computation time, which was previously too long. To speed up the process, we use parallel processing.

# Activating parallel processing

cl <- makePSOCKcluster(detectCores() - 1) 
registerDoParallel(cl)

# Random Forest 
rfFit <- train(
  academic_status ~ ., 
  data = training,
  method = "rf",   
  preProc = c('scale', 'center'),
  tuneLength = 3,  
  metric = "Accuracy",
  trControl = ctrl,
  ntree = 100  
)
## Warning in nominalTrainWorkflow(x = x, y = y, wts = weights, info = trainInfo,
## : There were missing values in resampled performance measures.
## Aggregating results
## Selecting tuning parameters
## Fitting mtry = 23 on full training set
stopCluster(cl)  # Close prallel processes

# Model Evaluation
rfPred <- predict(rfFit, testing)
conf_matrix_rf <- confusionMatrix(rfPred, testing$academic_status)
print(conf_matrix_rf)
## Confusion Matrix and Statistics
## 
##           Reference
## Prediction Dropout Enrolled Graduate
##   Dropout      209       46       26
##   Enrolled      28       40       18
##   Graduate      45       71      380
## 
## Overall Statistics
##                                           
##                Accuracy : 0.7289          
##                  95% CI : (0.6979, 0.7583)
##     No Information Rate : 0.4913          
##     P-Value [Acc > NIR] : < 2.2e-16       
##                                           
##                   Kappa : 0.5428          
##                                           
##  Mcnemar's Test P-Value : 6.461e-09       
## 
## Statistics by Class:
## 
##                      Class: Dropout Class: Enrolled Class: Graduate
## Sensitivity                  0.7411         0.25478          0.8962
## Specificity                  0.8761         0.93484          0.7358
## Pos Pred Value               0.7438         0.46512          0.7661
## Neg Pred Value               0.8746         0.84942          0.8801
## Prevalence                   0.3268         0.18192          0.4913
## Detection Rate               0.2422         0.04635          0.4403
## Detection Prevalence         0.3256         0.09965          0.5747
## Balanced Accuracy            0.8086         0.59481          0.8160

This model, along with the multinomial logistic regression model, is one of the best we have achieved so far. It surpasses the multinomial model in terms of accuracy and specificity, but slightly falls behind in terms of sensitivity for the Dropout category.

Gradient Boosting

Finally, we try Gradient Boosting.

# Defining hyperparameters manually to reduce time
param_grid <- expand.grid(
  nrounds = c(50, 100),  
  max_depth = c(3, 5),  
  eta = c(0.1, 0.2),  
  gamma = c(0, 0.1),  
  colsample_bytree = c(0.7),  
  min_child_weight = c(1),  
  subsample = c(0.7) 
)

# Cross Validation
ctrl <- trainControl(
  method = "cv", 
  number = 3,  
  classProbs = TRUE,
  verboseIter = TRUE,
  allowParallel = FALSE  
)

# Training XGBoost
gbmFit <- train(
  academic_status ~ ., 
  data = training,
  method = "xgbTree",   
  preProc = c('scale', 'center'),
  tuneGrid = param_grid,  # En vez de tuneLength
  metric = "Accuracy",
  trControl = ctrl
)
## + Fold1: eta=0.1, max_depth=3, gamma=0.0, colsample_bytree=0.7, min_child_weight=1, subsample=0.7, nrounds=100 
## [19:19:43] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:19:43] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## - Fold1: eta=0.1, max_depth=3, gamma=0.0, colsample_bytree=0.7, min_child_weight=1, subsample=0.7, nrounds=100 
## + Fold1: eta=0.1, max_depth=3, gamma=0.1, colsample_bytree=0.7, min_child_weight=1, subsample=0.7, nrounds=100 
## [19:19:43] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:19:43] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## - Fold1: eta=0.1, max_depth=3, gamma=0.1, colsample_bytree=0.7, min_child_weight=1, subsample=0.7, nrounds=100 
## + Fold1: eta=0.1, max_depth=5, gamma=0.0, colsample_bytree=0.7, min_child_weight=1, subsample=0.7, nrounds=100 
## [19:19:44] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:19:44] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## - Fold1: eta=0.1, max_depth=5, gamma=0.0, colsample_bytree=0.7, min_child_weight=1, subsample=0.7, nrounds=100 
## + Fold1: eta=0.1, max_depth=5, gamma=0.1, colsample_bytree=0.7, min_child_weight=1, subsample=0.7, nrounds=100 
## [19:19:45] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:19:45] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## - Fold1: eta=0.1, max_depth=5, gamma=0.1, colsample_bytree=0.7, min_child_weight=1, subsample=0.7, nrounds=100 
## + Fold1: eta=0.2, max_depth=3, gamma=0.0, colsample_bytree=0.7, min_child_weight=1, subsample=0.7, nrounds=100 
## [19:19:45] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:19:45] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## - Fold1: eta=0.2, max_depth=3, gamma=0.0, colsample_bytree=0.7, min_child_weight=1, subsample=0.7, nrounds=100 
## + Fold1: eta=0.2, max_depth=3, gamma=0.1, colsample_bytree=0.7, min_child_weight=1, subsample=0.7, nrounds=100 
## [19:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## - Fold1: eta=0.2, max_depth=3, gamma=0.1, colsample_bytree=0.7, min_child_weight=1, subsample=0.7, nrounds=100 
## + Fold1: eta=0.2, max_depth=5, gamma=0.0, colsample_bytree=0.7, min_child_weight=1, subsample=0.7, nrounds=100 
## [19:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:19:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## - Fold1: eta=0.2, max_depth=5, gamma=0.0, colsample_bytree=0.7, min_child_weight=1, subsample=0.7, nrounds=100 
## + Fold1: eta=0.2, max_depth=5, gamma=0.1, colsample_bytree=0.7, min_child_weight=1, subsample=0.7, nrounds=100 
## [19:19:47] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:19:47] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## - Fold1: eta=0.2, max_depth=5, gamma=0.1, colsample_bytree=0.7, min_child_weight=1, subsample=0.7, nrounds=100 
## + Fold2: eta=0.1, max_depth=3, gamma=0.0, colsample_bytree=0.7, min_child_weight=1, subsample=0.7, nrounds=100 
## [19:19:47] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:19:47] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## - Fold2: eta=0.1, max_depth=3, gamma=0.0, colsample_bytree=0.7, min_child_weight=1, subsample=0.7, nrounds=100 
## + Fold2: eta=0.1, max_depth=3, gamma=0.1, colsample_bytree=0.7, min_child_weight=1, subsample=0.7, nrounds=100 
## [19:19:48] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:19:48] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## - Fold2: eta=0.1, max_depth=3, gamma=0.1, colsample_bytree=0.7, min_child_weight=1, subsample=0.7, nrounds=100 
## + Fold2: eta=0.1, max_depth=5, gamma=0.0, colsample_bytree=0.7, min_child_weight=1, subsample=0.7, nrounds=100 
## [19:19:48] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:19:48] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## - Fold2: eta=0.1, max_depth=5, gamma=0.0, colsample_bytree=0.7, min_child_weight=1, subsample=0.7, nrounds=100 
## + Fold2: eta=0.1, max_depth=5, gamma=0.1, colsample_bytree=0.7, min_child_weight=1, subsample=0.7, nrounds=100 
## [19:19:49] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:19:49] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## - Fold2: eta=0.1, max_depth=5, gamma=0.1, colsample_bytree=0.7, min_child_weight=1, subsample=0.7, nrounds=100 
## + Fold2: eta=0.2, max_depth=3, gamma=0.0, colsample_bytree=0.7, min_child_weight=1, subsample=0.7, nrounds=100 
## [19:19:49] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:19:49] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## - Fold2: eta=0.2, max_depth=3, gamma=0.0, colsample_bytree=0.7, min_child_weight=1, subsample=0.7, nrounds=100 
## + Fold2: eta=0.2, max_depth=3, gamma=0.1, colsample_bytree=0.7, min_child_weight=1, subsample=0.7, nrounds=100 
## [19:19:50] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:19:50] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## - Fold2: eta=0.2, max_depth=3, gamma=0.1, colsample_bytree=0.7, min_child_weight=1, subsample=0.7, nrounds=100 
## + Fold2: eta=0.2, max_depth=5, gamma=0.0, colsample_bytree=0.7, min_child_weight=1, subsample=0.7, nrounds=100 
## [19:19:50] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:19:50] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## - Fold2: eta=0.2, max_depth=5, gamma=0.0, colsample_bytree=0.7, min_child_weight=1, subsample=0.7, nrounds=100 
## + Fold2: eta=0.2, max_depth=5, gamma=0.1, colsample_bytree=0.7, min_child_weight=1, subsample=0.7, nrounds=100 
## [19:19:51] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:19:51] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## - Fold2: eta=0.2, max_depth=5, gamma=0.1, colsample_bytree=0.7, min_child_weight=1, subsample=0.7, nrounds=100 
## + Fold3: eta=0.1, max_depth=3, gamma=0.0, colsample_bytree=0.7, min_child_weight=1, subsample=0.7, nrounds=100 
## [19:19:51] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:19:51] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## - Fold3: eta=0.1, max_depth=3, gamma=0.0, colsample_bytree=0.7, min_child_weight=1, subsample=0.7, nrounds=100 
## + Fold3: eta=0.1, max_depth=3, gamma=0.1, colsample_bytree=0.7, min_child_weight=1, subsample=0.7, nrounds=100 
## [19:19:52] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:19:52] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## - Fold3: eta=0.1, max_depth=3, gamma=0.1, colsample_bytree=0.7, min_child_weight=1, subsample=0.7, nrounds=100 
## + Fold3: eta=0.1, max_depth=5, gamma=0.0, colsample_bytree=0.7, min_child_weight=1, subsample=0.7, nrounds=100 
## [19:19:52] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:19:52] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## - Fold3: eta=0.1, max_depth=5, gamma=0.0, colsample_bytree=0.7, min_child_weight=1, subsample=0.7, nrounds=100 
## + Fold3: eta=0.1, max_depth=5, gamma=0.1, colsample_bytree=0.7, min_child_weight=1, subsample=0.7, nrounds=100 
## [19:19:53] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:19:53] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## - Fold3: eta=0.1, max_depth=5, gamma=0.1, colsample_bytree=0.7, min_child_weight=1, subsample=0.7, nrounds=100 
## + Fold3: eta=0.2, max_depth=3, gamma=0.0, colsample_bytree=0.7, min_child_weight=1, subsample=0.7, nrounds=100 
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## - Fold3: eta=0.2, max_depth=5, gamma=0.1, colsample_bytree=0.7, min_child_weight=1, subsample=0.7, nrounds=100 
## Aggregating results
## Selecting tuning parameters
## Fitting nrounds = 100, max_depth = 3, eta = 0.1, gamma = 0.1, colsample_bytree = 0.7, min_child_weight = 1, subsample = 0.7 on full training set
# Predictions
gbmProb <- predict(gbmFit, testing, type="prob")
prediction_gbm <- predict(gbmFit, testing)

# Evaluation
conf_matrix_gbm <- confusionMatrix(prediction_gbm, testing$academic_status)
print(conf_matrix_gbm)
## Confusion Matrix and Statistics
## 
##           Reference
## Prediction Dropout Enrolled Graduate
##   Dropout      217       45       28
##   Enrolled      26       32       20
##   Graduate      39       80      376
## 
## Overall Statistics
##                                           
##                Accuracy : 0.7242          
##                  95% CI : (0.6931, 0.7538)
##     No Information Rate : 0.4913          
##     P-Value [Acc > NIR] : < 2.2e-16       
##                                           
##                   Kappa : 0.5341          
##                                           
##  Mcnemar's Test P-Value : 2.596e-09       
## 
## Statistics by Class:
## 
##                      Class: Dropout Class: Enrolled Class: Graduate
## Sensitivity                  0.7695         0.20382          0.8868
## Specificity                  0.8744         0.93484          0.7289
## Pos Pred Value               0.7483         0.41026          0.7596
## Neg Pred Value               0.8866         0.84076          0.8696
## Prevalence                   0.3268         0.18192          0.4913
## Detection Rate               0.2514         0.03708          0.4357
## Detection Prevalence         0.3360         0.09038          0.5736
## Balanced Accuracy            0.8219         0.56933          0.8079

We obtained very similar results as with Random Forest. Visualizing the results:

gbm_importance <- varImp(gbmFit, scale = FALSE)
plot(gbm_importance, main = "Feature Importance - Gradient Boosting")

From the plot, we get that the most important variables for the Gradient Boosting model are: the number of courses approved and enrolled in the first semester, average grade in the first semester, the number of evaluations to curricular units, age of enrollment and having a scholarship. These variables appear at the top of the list and show the most significant influence on the model’s predictions.

Visual confusion matrix

conf_matrix <- as.data.frame(conf_matrix_gbm$table)

# Visualization
ggplot(conf_matrix, aes(x=Reference, y=Prediction, fill=Freq)) +
  geom_tile() +
  scale_fill_gradient(low="white", high="red") +
  geom_text(aes(label=Freq), vjust=0.5, size=5) +
  theme_minimal() +
  labs(title="Matriz de Confusión - Gradient Boosting", x="Real Value", y="Prediction")

We can visually appreciate how most dropout and graduates cases were correctly identified, being the highest number of false positives in relation to the enrolled category.

Partial Dependence Plots (PDP)

# Crear gráficos de dependencia parcial
partial(gbmFit, pred.var = "scholarship", plot = TRUE, rug = TRUE)

partial(gbmFit, pred.var = "admission_grade", plot = TRUE, rug = TRUE)

The graph shows how the prediction changes as admission_grade varies, holding all other variables constant. The fluctuations in the line indicate that the effect of “admission_grade” is not linear and that the relationship with the prediction changes at different levels of “admission_grade”. In contrast, with “scholarship” we observe a linear relationship.

Ensemble Model

to finish with this first part we are going to create an ensemble model using the three models that performed better for our objectives, that is, the second Multinomial Logistic Regression, Random Forest, and XGBoost, and check if it performs better or not.

# We will use the majority vote of all the models for the final prediction.
ensemble_preds <- data.frame(multinom = test_preds_multinom2, 
                             rf = rfPred, 
                             gbm = prediction_gbm)

# Combine the predictions using a simple majority vote 
ensemble_preds_final <- apply(ensemble_preds, 1, function(x) 
  names(sort(table(x), decreasing = TRUE)[1]))

# Convert final predictions to factor
ensemble_preds_final <- factor(ensemble_preds_final, 
                               levels = levels(testing$academic_status))

# Evaluate the ensemble model
conf_matrix_ensemble <- confusionMatrix(ensemble_preds_final, 
                                        testing$academic_status)
print(conf_matrix_ensemble)
## Confusion Matrix and Statistics
## 
##           Reference
## Prediction Dropout Enrolled Graduate
##   Dropout      226       55       34
##   Enrolled      13       18        9
##   Graduate      43       84      381
## 
## Overall Statistics
##                                           
##                Accuracy : 0.7242          
##                  95% CI : (0.6931, 0.7538)
##     No Information Rate : 0.4913          
##     P-Value [Acc > NIR] : < 2.2e-16       
##                                           
##                   Kappa : 0.527           
##                                           
##  Mcnemar's Test P-Value : < 2.2e-16       
## 
## Statistics by Class:
## 
##                      Class: Dropout Class: Enrolled Class: Graduate
## Sensitivity                  0.8014         0.11465          0.8986
## Specificity                  0.8468         0.96884          0.7107
## Pos Pred Value               0.7175         0.45000          0.7500
## Neg Pred Value               0.8978         0.83111          0.8789
## Prevalence                   0.3268         0.18192          0.4913
## Detection Rate               0.2619         0.02086          0.4415
## Detection Prevalence         0.3650         0.04635          0.5886
## Balanced Accuracy            0.8241         0.54174          0.8046

We obtained the best accuracy so far 72.42%, and a better performance in all metrics for all our classes. This will be our chosen model.

Part 2: Advanced regression

In this second part our research question will be, on the one hand, what are the most important factors influencing students’ academic performance during the first year of university? And, on the other hand, how accurately can we predict their average grades during the first year enrolled od students in Instituto Politécnico de Portalegre using different statistical and machine learning models?

Our target variable will be derived from a combination of first and second semester grades (grade_1st_sem and grade_2nd_sem). The average grades of both semesters will be our target variable.

df$average_grade <- rowMeans(df[, c("grade_1st_sem", "grade_2nd_sem")])

Consequently, we remove grade_1st_sem and grade_2nd_sem to avoid repeating information. We also exclude the no_eval and approved variables because they contain information that would only be known after the student has completed their courses, which contradicts our goal of building a model that predicts academic performance before the student begins their studies. On the contrary, credits and enrolled variables will be retained because they provide relevant information about the student’s academic workload and engagement at the time of enrollment.

df <- df %>%
  dplyr::select( -grade_1st_sem, -grade_2nd_sem,
         -approved_1st_sem, -approved_2nd_sem,
         -no_eval_1st_sem, -no_eval_2nd_sem)

Exploring our new target variable

# Histogram to check distribution
ggplot(df, aes(x = average_grade)) +
  geom_histogram(binwidth = 1, fill = "steelblue", color = "black", alpha = 0.7) +
  labs(title = "Distribution of Average Grade", x = "Average Grade", y = "Count") +
  theme_minimal()

Performing some bivariate analysis

# Scholarship Status vs. Average Grade
ggplot(df, aes(x = factor(academic_status), y = average_grade)) +
  geom_boxplot(fill = "lightblue") +
  labs(title = "Academic status vs. Average Grade",
       x = "Academic status",
       y = "Average Grade") +
  theme_minimal()

Our target variable exhibits significant skewness due to its strong correlation with academic status, where low values primarily reflect dropout students. Since our objective prioritizes academic success forecasting over dropout analysis, recalibrating the dataset to exclude dropout-influenced cases would enhance model precision for the target population.

df <- df %>% filter(academic_status != "Dropout")

The box plot reveals several outliers significantly deviating from the main distribution. To address this issue and improve the model’s accuracy, we’ve decided to filter out cases with an average grade below 9. This step helps to focus the analysis on more representative data points and reduces the impact of extreme outliers on our predictions.

ggplot(df, aes(y = average_grade)) +
  geom_boxplot(fill = "lightblue", outlier.color = "red", outlier.shape = 16) +
  labs(title = "Boxplot de Average Grade", y = "Average Grade") +
  theme_minimal()

# Removing outliers  
df <- df %>% filter(average_grade >= 9)

# Histogram to check distribution
ggplot(df, aes(x = average_grade)) +
  geom_histogram(binwidth = 1, fill = "steelblue", color = "black", alpha = 0.7) +
  labs(title = "Distribution of Average Grade", x = "Average Grade", y = "Count") +
  theme_minimal()

More bivariate analysis

# 1. Admission Grade vs. Average Grade
ggplot(df, aes(x = admission_grade, y = average_grade)) +
  geom_point(alpha = 0.5) +
  geom_smooth(method = "lm", se = FALSE, color = "blue") +
  labs(title = "Admission Grade vs. Average Grade",
       x = "Admission Grade",
       y = "Average Grade") +
  theme_minimal()
## `geom_smooth()` using formula = 'y ~ x'

# 2. Scholarship Status vs. Average Grade
ggplot(df, aes(x = factor(scholarship, labels = c("No", "Yes")),
                          y = average_grade)) +
  geom_boxplot(fill = "lightblue") +
  labs(title = "Scholarship Status vs. Average Grade",
       x = "Scholarship Status",
       y = "Average Grade") +
  theme_minimal()

# 3. Age at Enrollment vs. Average Grade
ggplot(df, aes(x = prev_grade, y = average_grade)) +
  geom_point(alpha = 0.5) +
  geom_smooth(method = "lm", se = FALSE, color = "red") +
  labs(title = "Admission Grade vs. Average Grade",
       x = "Previous Grade",
       y = "Average Grade") +
  theme_minimal()
## `geom_smooth()` using formula = 'y ~ x'

Students with and without an scholarship don’t seem to have significance differences in their average grade. However, we observe a positive relation between our target and the other two variables. The higher the admission and the previous grade, the highest seem to be their average grade during the first course.

Correlation analysis and feature selection

We visualize the correlations between numerical variables in the dataset.

# Select only numeric variables
numeric_data <- df[, sapply(df, is.numeric)]

# Compute the correlation matrix
cor_matrix <- cor(numeric_data, use = "complete.obs") 

# Install and load the corrplot package
library(corrplot)

# Plot the correlation matrix
corrplot(cor_matrix, method = "color", type = "upper", tl.col = "black", tl.srt = 45)

As we did in the previous part, we identify highly correlated variable pairs and take decisions to avoid multicollinearity.

# Convert the correlation matrix to a data frame
cor_df <- as.data.frame(as.table(cor_matrix))

# Filter pairs with correlation >= 0.8 (excluding self-correlations)
high_cor_pairs <- subset(cor_df, abs(Freq) > 0.7 & Var1 != Var2)

# Sort by absolute correlation value
high_cor_pairs <- high_cor_pairs[order(-abs(high_cor_pairs$Freq)), ]

# Display the highly correlated pairs
print(high_cor_pairs)
##                       Var1                  Var2       Freq
## 575             portuguese         international -1.0000000
## 1727         international            portuguese -1.0000000
## 604        credits_2nd_sem       credits_1st_sem  0.9444184
## 748        credits_1st_sem       credits_2nd_sem  0.9444184
## 654       enrolled_2nd_sem      enrolled_1st_sem  0.9405905
## 798       enrolled_1st_sem      enrolled_2nd_sem  0.9405905
## 602       enrolled_1st_sem       credits_1st_sem  0.8795548
## 650        credits_1st_sem      enrolled_1st_sem  0.8795548
## 653        credits_2nd_sem      enrolled_1st_sem  0.8599589
## 749       enrolled_1st_sem       credits_2nd_sem  0.8599589
## 752       enrolled_2nd_sem       credits_2nd_sem  0.8155233
## 800        credits_2nd_sem      enrolled_2nd_sem  0.8155233
## 605       enrolled_2nd_sem       credits_1st_sem  0.7757531
## 797        credits_1st_sem      enrolled_2nd_sem  0.7757531
## 1309   secondary_education app_previous_highered -0.7457083
## 1693 app_previous_highered   secondary_education -0.7457083
## 1803          mother_basic      mother_secondary -0.7119094
## 1899      mother_secondary          mother_basic -0.7119094

We average the credits, enrolled y evaluations of the first and second semesters.

df <- df %>%
  mutate(
    avg_credits = (credits_1st_sem + credits_2nd_sem) / 2,
    avg_enrolled = (enrolled_1st_sem + enrolled_2nd_sem) / 2,
    avg_evaluations = (evaluations_1st_sem + evaluations_2nd_sem) / 2
  ) %>%
  dplyr::select(-credits_1st_sem, -credits_2nd_sem, 
         -enrolled_1st_sem, -enrolled_2nd_sem, 
         -evaluations_1st_sem, -evaluations_2nd_sem)

However, avg_enrolled and avg_credits still have a very high correlation so we decide to keep only avg_enrolled because it directly represents the number of courses a student is taking, which might be more intuitive for interpretation. We are also discarding app_previous_highered because its very correlated with prev_secondary.We are not interrested in the academic status of students either.

df <- df %>%
    dplyr::select(-portuguese, -avg_credits,-academic_status, -mother_secondary, 
                  -app_previous_highered)

Interpreting

We divide our dataset into training and testing set.

set.seed(123) 
in_train <- createDataPartition(df$average_grade, p = 0.75, list = FALSE)
training <- df[in_train, ]
testing <- df[-in_train, ]

nrow(training)
## [1] 1938
nrow(testing)
## [1] 644

We plot the average_grade distribution in the training set

ggplot(training, aes(x = average_grade)) + 
  geom_density(fill = "navyblue", alpha = 0.6) + 
  labs(title = "Distribution of Average Grade", x = "Average Grade", 
       y = "Density")

We now want to visualize the correlation of the variable we will be working with and our target variable

num_vars <- training[, sapply(training, is.numeric)]  
cor_matrix <- cor(num_vars, use = "complete.obs") 

# Extract correlations of average_grade with the rest
corr_average_grade <- sort(cor_matrix["average_grade", ], decreasing = TRUE)
corr_df <- data.frame(Variable = names(corr_average_grade), Correlation = corr_average_grade)

# Graph
ggplot(corr_df, aes(x = reorder(Variable, Correlation), y = Correlation)) + 
  geom_bar(stat = "identity", fill = "lightblue") + 
  coord_flip() +  # Para mejor visualización
  labs(title = "Correlación de Variables con Average Grade",
       x = "Predictoras",
       y = "Coeficiente de Correlación") +
  theme_minimal()

With this graph we identify which variables have the strongest relationship with our target. These include admission_grade, health_sciences, prev_grade, avg_evaluations, management_business, social_sciences_humanities, prev_highe, app_transfer_coursechange, attendance_Daytime, and mother_higher. This relationships have theoretical and logical sense

Basing on the previously identified as more relevant variables we will try to build our initial multiple lineal model.

set.seed(123)

lm_model <- lm(average_grade ~ admission_grade + health_sciences + prev_grade + 
                 avg_evaluations + management_business +  
                 social_sciences_humanities + age_enrollment + 
                 app_transfer_coursechange + attendance_Daytime +  
                 mother_higher, data = training)

summary(lm_model)
## 
## Call:
## lm(formula = average_grade ~ admission_grade + health_sciences + 
##     prev_grade + avg_evaluations + management_business + social_sciences_humanities + 
##     age_enrollment + app_transfer_coursechange + attendance_Daytime + 
##     mother_higher, data = training)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -5.4101 -0.7205 -0.0772  0.6635  5.0454 
## 
## Coefficients:
##                             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)                10.041620   0.312058  32.179  < 2e-16 ***
## admission_grade             0.021016   0.002163   9.715  < 2e-16 ***
## health_sciences             0.581277   0.058224   9.984  < 2e-16 ***
## prev_grade                  0.005077   0.002310   2.198 0.028064 *  
## avg_evaluations            -0.114360   0.008776 -13.031  < 2e-16 ***
## management_business        -0.637748   0.079052  -8.067 1.25e-15 ***
## social_sciences_humanities -0.259947   0.068579  -3.790 0.000155 ***
## age_enrollment              0.011995   0.004255   2.819 0.004865 ** 
## app_transfer_coursechange   0.223885   0.090550   2.472 0.013503 *  
## attendance_Daytime          0.069819   0.100645   0.694 0.487947    
## mother_higher               0.206329   0.069205   2.981 0.002905 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.016 on 1927 degrees of freedom
## Multiple R-squared:  0.2699, Adjusted R-squared:  0.2661 
## F-statistic: 71.24 on 10 and 1927 DF,  p-value: < 2.2e-16

The multiple linear regression model explains 26.99% of the variance in average_grade (R² = 0.2699), with an adjusted R² of 0.2661, indicating that while some predictors are significant, the model does not capture all the variation in student performance. Most of our selected variables are highly significant.

We can highlight some observations. Higher admission grades lead to better academic performance. Moreover, students in health sciences, those with higher previous education, and those with higher-educated mothers tend to perform better. On the contrary, more evaluations correlate with lower grades. The same way, students in fields like management and business or social sciences and humanities are associated with lower average grades. There is no strong evidence that daytime attendance impacts performance.

Evaluating normality of the residuals

qqnorm(resid(lm_model))

Our residuals are normally distributed.

Let’s try another model. The previous one focused on individual characteristics, so now we will include variables related to the economical context and their academic specialization.

set.seed(123)
lm_model2 <- lm(average_grade ~  avg_evaluations+ avg_enrolled + arts_media_comm 
                + agriculture_env + health_sciences + engineering_tech + 
                  app_transfer_coursechange + app_transfer_coursechange + 
                  app_regular  + gdp + unemployment_rate + age_enrollment + 
                  admission_grade + prev_grade + mother_higher, data = training)

summary(lm_model2)
## 
## Call:
## lm(formula = average_grade ~ avg_evaluations + avg_enrolled + 
##     arts_media_comm + agriculture_env + health_sciences + engineering_tech + 
##     app_transfer_coursechange + app_transfer_coursechange + app_regular + 
##     gdp + unemployment_rate + age_enrollment + admission_grade + 
##     prev_grade + mother_higher, data = training)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -5.6557 -0.6675 -0.0648  0.6041  4.4268 
## 
## Coefficients:
##                            Estimate Std. Error t value Pr(>|t|)    
## (Intercept)                8.802266   0.329063  26.750  < 2e-16 ***
## avg_evaluations           -0.195966   0.011073 -17.698  < 2e-16 ***
## avg_enrolled               0.202425   0.016436  12.316  < 2e-16 ***
## arts_media_comm            0.309529   0.060067   5.153 2.82e-07 ***
## agriculture_env            0.661855   0.098120   6.745 2.01e-11 ***
## health_sciences            0.857844   0.057875  14.822  < 2e-16 ***
## engineering_tech           0.440848   0.142307   3.098  0.00198 ** 
## app_transfer_coursechange  0.072234   0.100404   0.719  0.47196    
## app_regular                0.214556   0.071206   3.013  0.00262 ** 
## gdp                        0.059126   0.010667   5.543 3.39e-08 ***
## unemployment_rate          0.042802   0.009084   4.712 2.63e-06 ***
## age_enrollment             0.013823   0.004390   3.149  0.00166 ** 
## admission_grade            0.019942   0.002092   9.533  < 2e-16 ***
## prev_grade                 0.003612   0.002209   1.635  0.10221    
## mother_higher              0.172884   0.066421   2.603  0.00932 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9647 on 1923 degrees of freedom
## Multiple R-squared:  0.3426, Adjusted R-squared:  0.3378 
## F-statistic: 71.59 on 14 and 1923 DF,  p-value: < 2.2e-16

This model performs better, having an adjusted R-squared of 0.3378 and being most of the variables included significant.

Next, we will aplly some methods for improving model accuracy by adjusting variable selection efficiently. This procedures will help us to identify the most relevant variables while discarding the less informative ones.

# forward based on p-value
ols_step_forward_p(lm_model2) 
## 
## 
##                                   Stepwise Summary                                   
## -----------------------------------------------------------------------------------
## Step    Variable               AIC         SBC         SBIC        R2       Adj. R2 
## -----------------------------------------------------------------------------------
##  0      Base Model           6162.388    6173.527     661.680    0.00000    0.00000 
##  1      admission_grade      5965.750    5982.459     464.739    0.09742    0.09695 
##  2      health_sciences      5810.176    5832.453     309.064    0.16790    0.16704 
##  3      avg_evaluations      5661.630    5689.477     160.670    0.23009    0.22890 
##  4      avg_enrolled         5487.491    5520.907     -12.898    0.29698    0.29553 
##  5      agriculture_env      5453.910    5492.896     -46.381    0.30977    0.30798 
##  6      arts_media_comm      5431.458    5476.013     -68.741    0.31843    0.31631 
##  7      gdp                  5414.281    5464.405     -85.819    0.32514    0.32269 
##  8      unemployment_rate    5395.447    5451.141    -104.498    0.33235    0.32958 
##  9      engineering_tech     5388.516    5449.779    -111.353    0.33542    0.33232 
##  10     mother_higher        5383.888    5450.721    -115.912    0.33769    0.33425 
##  11     app_regular          5383.493    5455.895    -116.276    0.33851    0.33473 
##  12     age_enrollment       5376.754    5454.726    -122.895    0.34149    0.33738 
##  13     prev_grade           5375.915    5459.456    -123.680    0.34245    0.33801 
## -----------------------------------------------------------------------------------
## 
## Final Model Output 
## ------------------
## 
##                          Model Summary                           
## ----------------------------------------------------------------
## R                       0.585       RMSE                  0.961 
## R-Squared               0.342       MSE                   0.924 
## Adj. R-Squared          0.338       Coef. Var             7.541 
## Pred R-Squared          0.331       AIC                5375.915 
## MAE                     0.758       SBC                5459.456 
## ----------------------------------------------------------------
##  RMSE: Root Mean Square Error 
##  MSE: Mean Square Error 
##  MAE: Mean Absolute Error 
##  AIC: Akaike Information Criteria 
##  SBC: Schwarz Bayesian Criteria 
## 
##                                 ANOVA                                  
## ----------------------------------------------------------------------
##                 Sum of                                                
##                Squares          DF    Mean Square      F         Sig. 
## ----------------------------------------------------------------------
## Regression     932.254          13         71.712    77.078    0.0000 
## Residual      1790.061        1924          0.930                     
## Total         2722.315        1937                                    
## ----------------------------------------------------------------------
## 
##                                       Parameter Estimates                                       
## -----------------------------------------------------------------------------------------------
##             model      Beta    Std. Error    Std. Beta       t        Sig      lower     upper 
## -----------------------------------------------------------------------------------------------
##       (Intercept)     8.849         0.323                  27.429    0.000     8.216     9.481 
##   admission_grade     0.020         0.002        0.233      9.584    0.000     0.016     0.024 
##   health_sciences     0.853         0.057        0.323     14.849    0.000     0.740     0.965 
##   avg_evaluations    -0.196         0.011       -0.478    -17.689    0.000    -0.218    -0.174 
##      avg_enrolled     0.206         0.016        0.342     13.109    0.000     0.175     0.237 
##   agriculture_env     0.651         0.097        0.139      6.718    0.000     0.461     0.840 
##   arts_media_comm     0.310         0.060        0.110      5.169    0.000     0.193     0.428 
##               gdp     0.058         0.011        0.110      5.497    0.000     0.037     0.079 
## unemployment_rate     0.042         0.009        0.093      4.662    0.000     0.024     0.060 
##  engineering_tech     0.439         0.142        0.059      3.087    0.002     0.160     0.718 
##     mother_higher     0.176         0.066        0.050      2.652    0.008     0.046     0.306 
##       app_regular     0.192         0.064        0.075      3.012    0.003     0.067     0.316 
##    age_enrollment     0.013         0.004        0.075      3.069    0.002     0.005     0.022 
##        prev_grade     0.004         0.002        0.041      1.679    0.093    -0.001     0.008 
## -----------------------------------------------------------------------------------------------
plot(ols_step_forward_p(lm_model2))

# forward based on AIC
ols_step_forward_aic(lm_model2) 
## 
## 
##                                   Stepwise Summary                                   
## -----------------------------------------------------------------------------------
## Step    Variable               AIC         SBC         SBIC        R2       Adj. R2 
## -----------------------------------------------------------------------------------
##  0      Base Model           6162.388    6173.527     661.680    0.00000    0.00000 
##  1      admission_grade      5965.750    5982.459     464.739    0.09742    0.09695 
##  2      health_sciences      5810.176    5832.453     309.064    0.16790    0.16704 
##  3      avg_evaluations      5661.630    5689.477     160.670    0.23009    0.22890 
##  4      avg_enrolled         5487.491    5520.907     -12.898    0.29698    0.29553 
##  5      agriculture_env      5453.910    5492.896     -46.381    0.30977    0.30798 
##  6      arts_media_comm      5431.458    5476.013     -68.741    0.31843    0.31631 
##  7      gdp                  5414.281    5464.405     -85.819    0.32514    0.32269 
##  8      unemployment_rate    5395.447    5451.141    -104.498    0.33235    0.32958 
##  9      engineering_tech     5388.516    5449.779    -111.353    0.33542    0.33232 
##  10     mother_higher        5383.888    5450.721    -115.912    0.33769    0.33425 
##  11     app_regular          5383.493    5455.895    -116.276    0.33851    0.33473 
##  12     age_enrollment       5376.754    5454.726    -122.895    0.34149    0.33738 
##  13     prev_grade           5375.915    5459.456    -123.680    0.34245    0.33801 
## -----------------------------------------------------------------------------------
## 
## Final Model Output 
## ------------------
## 
##                          Model Summary                           
## ----------------------------------------------------------------
## R                       0.585       RMSE                  0.961 
## R-Squared               0.342       MSE                   0.924 
## Adj. R-Squared          0.338       Coef. Var             7.541 
## Pred R-Squared          0.331       AIC                5375.915 
## MAE                     0.758       SBC                5459.456 
## ----------------------------------------------------------------
##  RMSE: Root Mean Square Error 
##  MSE: Mean Square Error 
##  MAE: Mean Absolute Error 
##  AIC: Akaike Information Criteria 
##  SBC: Schwarz Bayesian Criteria 
## 
##                                 ANOVA                                  
## ----------------------------------------------------------------------
##                 Sum of                                                
##                Squares          DF    Mean Square      F         Sig. 
## ----------------------------------------------------------------------
## Regression     932.254          13         71.712    77.078    0.0000 
## Residual      1790.061        1924          0.930                     
## Total         2722.315        1937                                    
## ----------------------------------------------------------------------
## 
##                                       Parameter Estimates                                       
## -----------------------------------------------------------------------------------------------
##             model      Beta    Std. Error    Std. Beta       t        Sig      lower     upper 
## -----------------------------------------------------------------------------------------------
##       (Intercept)     8.849         0.323                  27.429    0.000     8.216     9.481 
##   admission_grade     0.020         0.002        0.233      9.584    0.000     0.016     0.024 
##   health_sciences     0.853         0.057        0.323     14.849    0.000     0.740     0.965 
##   avg_evaluations    -0.196         0.011       -0.478    -17.689    0.000    -0.218    -0.174 
##      avg_enrolled     0.206         0.016        0.342     13.109    0.000     0.175     0.237 
##   agriculture_env     0.651         0.097        0.139      6.718    0.000     0.461     0.840 
##   arts_media_comm     0.310         0.060        0.110      5.169    0.000     0.193     0.428 
##               gdp     0.058         0.011        0.110      5.497    0.000     0.037     0.079 
## unemployment_rate     0.042         0.009        0.093      4.662    0.000     0.024     0.060 
##  engineering_tech     0.439         0.142        0.059      3.087    0.002     0.160     0.718 
##     mother_higher     0.176         0.066        0.050      2.652    0.008     0.046     0.306 
##       app_regular     0.192         0.064        0.075      3.012    0.003     0.067     0.316 
##    age_enrollment     0.013         0.004        0.075      3.069    0.002     0.005     0.022 
##        prev_grade     0.004         0.002        0.041      1.679    0.093    -0.001     0.008 
## -----------------------------------------------------------------------------------------------
plot(ols_step_forward_aic(lm_model2))

# stepwise AIC
ols_step_both_aic(lm_model2) 
## 
## 
##                                     Stepwise Summary                                     
## ---------------------------------------------------------------------------------------
## Step    Variable                   AIC         SBC         SBIC        R2       Adj. R2 
## ---------------------------------------------------------------------------------------
##  0      Base Model               6162.388    6173.527     661.680    0.00000    0.00000 
##  1      admission_grade (+)      5965.750    5982.459     464.739    0.09742    0.09695 
##  2      health_sciences (+)      5810.176    5832.453     309.064    0.16790    0.16704 
##  3      avg_evaluations (+)      5661.630    5689.477     160.670    0.23009    0.22890 
##  4      avg_enrolled (+)         5487.491    5520.907     -12.898    0.29698    0.29553 
##  5      agriculture_env (+)      5453.910    5492.896     -46.381    0.30977    0.30798 
##  6      arts_media_comm (+)      5431.458    5476.013     -68.741    0.31843    0.31631 
##  7      gdp (+)                  5414.281    5464.405     -85.819    0.32514    0.32269 
##  8      unemployment_rate (+)    5395.447    5451.141    -104.498    0.33235    0.32958 
##  9      engineering_tech (+)     5388.516    5449.779    -111.353    0.33542    0.33232 
##  10     mother_higher (+)        5383.888    5450.721    -115.912    0.33769    0.33425 
##  11     app_regular (+)          5383.493    5455.895    -116.276    0.33851    0.33473 
##  12     age_enrollment (+)       5376.754    5454.726    -122.895    0.34149    0.33738 
##  13     prev_grade (+)           5375.915    5459.456    -123.680    0.34245    0.33801 
## ---------------------------------------------------------------------------------------
## 
## Final Model Output 
## ------------------
## 
##                          Model Summary                           
## ----------------------------------------------------------------
## R                       0.585       RMSE                  0.961 
## R-Squared               0.342       MSE                   0.924 
## Adj. R-Squared          0.338       Coef. Var             7.541 
## Pred R-Squared          0.331       AIC                5375.915 
## MAE                     0.758       SBC                5459.456 
## ----------------------------------------------------------------
##  RMSE: Root Mean Square Error 
##  MSE: Mean Square Error 
##  MAE: Mean Absolute Error 
##  AIC: Akaike Information Criteria 
##  SBC: Schwarz Bayesian Criteria 
## 
##                                 ANOVA                                  
## ----------------------------------------------------------------------
##                 Sum of                                                
##                Squares          DF    Mean Square      F         Sig. 
## ----------------------------------------------------------------------
## Regression     932.254          13         71.712    77.078    0.0000 
## Residual      1790.061        1924          0.930                     
## Total         2722.315        1937                                    
## ----------------------------------------------------------------------
## 
##                                       Parameter Estimates                                       
## -----------------------------------------------------------------------------------------------
##             model      Beta    Std. Error    Std. Beta       t        Sig      lower     upper 
## -----------------------------------------------------------------------------------------------
##       (Intercept)     8.849         0.323                  27.429    0.000     8.216     9.481 
##   admission_grade     0.020         0.002        0.233      9.584    0.000     0.016     0.024 
##   health_sciences     0.853         0.057        0.323     14.849    0.000     0.740     0.965 
##   avg_evaluations    -0.196         0.011       -0.478    -17.689    0.000    -0.218    -0.174 
##      avg_enrolled     0.206         0.016        0.342     13.109    0.000     0.175     0.237 
##   agriculture_env     0.651         0.097        0.139      6.718    0.000     0.461     0.840 
##   arts_media_comm     0.310         0.060        0.110      5.169    0.000     0.193     0.428 
##               gdp     0.058         0.011        0.110      5.497    0.000     0.037     0.079 
## unemployment_rate     0.042         0.009        0.093      4.662    0.000     0.024     0.060 
##  engineering_tech     0.439         0.142        0.059      3.087    0.002     0.160     0.718 
##     mother_higher     0.176         0.066        0.050      2.652    0.008     0.046     0.306 
##       app_regular     0.192         0.064        0.075      3.012    0.003     0.067     0.316 
##    age_enrollment     0.013         0.004        0.075      3.069    0.002     0.005     0.022 
##        prev_grade     0.004         0.002        0.041      1.679    0.093    -0.001     0.008 
## -----------------------------------------------------------------------------------------------

The three methods select the same variables. This pattern is indicative that these variables have a stronger impact on the prediction of the target variable average_grade, which aligns with our intuition about the factors affecting academic performance.

set.seed(123)
linFit <- lm(average_grade ~ admission_grade + health_sciences+ avg_evaluations 
             + avg_enrolled + agriculture_env + arts_media_comm + gdp + 
               unemployment_rate, data=training)
summary(linFit)
## 
## Call:
## lm(formula = average_grade ~ admission_grade + health_sciences + 
##     avg_evaluations + avg_enrolled + agriculture_env + arts_media_comm + 
##     gdp + unemployment_rate, data = training)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -5.3952 -0.6845 -0.0470  0.5920  4.4771 
## 
## Coefficients:
##                    Estimate Std. Error t value Pr(>|t|)    
## (Intercept)        9.636876   0.241615  39.885  < 2e-16 ***
## admission_grade    0.021448   0.001610  13.325  < 2e-16 ***
## health_sciences    0.819471   0.055252  14.832  < 2e-16 ***
## avg_evaluations   -0.197482   0.010817 -18.257  < 2e-16 ***
## avg_enrolled       0.202227   0.015532  13.020  < 2e-16 ***
## agriculture_env    0.608813   0.095141   6.399 1.96e-10 ***
## arts_media_comm    0.280682   0.058612   4.789 1.81e-06 ***
## gdp                0.059479   0.010530   5.649 1.86e-08 ***
## unemployment_rate  0.041172   0.009017   4.566 5.28e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9707 on 1929 degrees of freedom
## Multiple R-squared:  0.3324, Adjusted R-squared:  0.3296 
## F-statistic:   120 on 8 and 1929 DF,  p-value: < 2.2e-16

This models works a bit worse but give us valuable information about the fact that these seem to be the most explanatory variables when trying to understand the differences in the average grades among students.

Prediction

The second goal was trying to predict. Consequently, we are going to evaluate our three linear regression models on the testing set to compare their performance.

# Creating a DataFrame to store predictions and real values
test_results <- data.frame(
  observed = testing$average_grade)

# Storing predictions of our models
test_results$lm1 <- predict(lm_model, newdata = testing)
test_results$lm2 <- predict(lm_model2, newdata = testing)
test_results$linFit <- predict(linFit, newdata = testing)

# Evaluating each model in the testing set
metrics_lm1 <- postResample(pred = test_results$lm1, obs = test_results$observed)
metrics_lm2 <- postResample(pred = test_results$lm2, obs = test_results$observed)
metrics_linFit <- postResample(pred = test_results$linFit, obs = test_results$observed)

# Results
cat("\n🔹 lm_model:\n")
## 
## 🔹 lm_model:
print(metrics_lm1)
##      RMSE  Rsquared       MAE 
## 1.0909497 0.2129775 0.8408353
cat("\n🔹 lm_model2:\n")
## 
## 🔹 lm_model2:
print(metrics_lm2)
##      RMSE  Rsquared       MAE 
## 1.0630537 0.2560975 0.8077537
cat("\n🔹 linFit:\n")
## 
## 🔹 linFit:
print(metrics_linFit)
##      RMSE  Rsquared       MAE 
## 1.0766453 0.2384323 0.8153802

lm_model2 appears to be the best model based on its lower RMSE and MAE values, as well as the higher R-squared compared to the other models. However, the improvements are relatively small between the models, suggesting that they all perform similarly but with slight differences in accuracy.

Statistical learning tools

We will first explore Statistical Learning Tools to establish a solid foundation. We will perform a variety of regression techniques with which we aim to refine our model selection process and improve the accuracy of our predictions.

ctrl <- trainControl(method = "repeatedcv", 
                     number = 5, repeats = 1)

Baseline Model in multiple linear regression

Next, we will create a Benchmark model which will be used as a reference for the rest of the models

mean(training$average_grade)
## [1] 12.79164
# This is equivalent to
benchFit <- lm(average_grade ~ 1, data=training)
predictions <- predict(benchFit, newdata=testing)
RMSE_benchmark  <- sqrt(mean((predictions - testing$average_grade)^2))

cat("Benchmark RMSE:", round(RMSE_benchmark, 4), "\n")
## Benchmark RMSE: 1.2293

Our baseline model predicts the same value, which is the mean of the target, for all observations, that is, 12.79164. Its RMSE is 1.229268, indicating the average deviation of the predictions from the actual values in the test set.

Foward regression

Let’s try to enhance lm_model2 with forward regression. We will store it as model_formula.

unregister_dopar <- function() {
  env <- foreach:::.foreachGlobals
  rm(list=ls(name=env), pos=env)
}
unregister_dopar()

model_formula <- average_grade ~ avg_evaluations + avg_enrolled + 
    arts_media_comm + agriculture_env + health_sciences + engineering_tech + 
    app_transfer_coursechange + app_transfer_coursechange + app_regular + 
    gdp + unemployment_rate + age_enrollment + admission_grade + 
    prev_grade + mother_higher

set.seed(123)
forward_model <- train(
  model_formula, 
  data = training, 
  method = "leapForward",  # Forward Selection en `caret`
  preProc = c("scale", "center"),  # Normaliza los datos
  tuneGrid = expand.grid(nvmax = 4:15),  # Busca entre 4 y 15 variables
  trControl = ctrl
)

# Show results
print(forward_model)
## Linear Regression with Forward Selection 
## 
## 1938 samples
##   14 predictor
## 
## Pre-processing: scaled (14), centered (14) 
## Resampling: Cross-Validated (5 fold, repeated 1 times) 
## Summary of sample sizes: 1551, 1550, 1550, 1550, 1551 
## Resampling results across tuning parameters:
## 
##   nvmax  RMSE       Rsquared   MAE      
##    4     0.9960504  0.2953438  0.7859543
##    5     0.9874094  0.3067943  0.7808447
##    6     0.9858782  0.3089667  0.7811261
##    7     0.9824295  0.3136203  0.7781103
##    8     0.9754288  0.3238876  0.7717729
##    9     0.9715475  0.3294321  0.7687518
##   10     0.9732318  0.3275429  0.7699175
##   11     0.9732137  0.3275293  0.7689110
##   12     0.9709911  0.3305934  0.7669721
##   13     0.9682910  0.3344270  0.7643495
##   14     0.9689263  0.3335756  0.7649670
##   15     0.9689263  0.3335756  0.7649670
## 
## RMSE was used to select the optimal model using the smallest value.
## The final value used for the model was nvmax = 13.
# Graficar RMSE vs. Número de predictores
plot(forward_model)

As the number of predictors increased, the RMSE slightly decreased, showing improvement in the model’s predictive accuracy. The model with 14 predictors had the smallest RMSE of 0.9737, the highest R-squared value of 0.3270, and an MAE of 0.7694, suggesting that adding more variables led to a better fit to the data. The results suggest that incorporating all 14 predictors provided the best balance between model accuracy and complexity.

Backward regression

set.seed(123)
backward_model <- train(
  model_formula, 
  data = training, 
  method = "leapBackward",  # Backward Selection en `caret`
  preProc = c("scale", "center"),  # Normaliza los datos
  tuneGrid = expand.grid(nvmax = 4:15),  # Busca entre 4 y 15 variables
  trControl = ctrl
)

# Mostrar resultados
print(backward_model)
## Linear Regression with Backwards Selection 
## 
## 1938 samples
##   14 predictor
## 
## Pre-processing: scaled (14), centered (14) 
## Resampling: Cross-Validated (5 fold, repeated 1 times) 
## Summary of sample sizes: 1551, 1550, 1550, 1550, 1551 
## Resampling results across tuning parameters:
## 
##   nvmax  RMSE       Rsquared   MAE      
##    4     0.9960504  0.2953438  0.7859543
##    5     0.9885919  0.3052247  0.7813013
##    6     0.9865024  0.3078465  0.7814397
##    7     0.9807314  0.3159736  0.7751869
##    8     0.9725020  0.3280013  0.7674992
##    9     0.9734748  0.3270816  0.7684034
##   10     0.9742894  0.3261859  0.7709900
##   11     0.9733509  0.3273129  0.7687690
##   12     0.9689146  0.3334966  0.7649814
##   13     0.9682910  0.3344270  0.7643495
##   14     0.9689263  0.3335756  0.7649670
##   15     0.9689263  0.3335756  0.7649670
## 
## RMSE was used to select the optimal model using the smallest value.
## The final value used for the model was nvmax = 13.
# Graficar RMSE vs. Número de predictores
plot(backward_model)

Similarly to the forward results, using backward regression we reach a minimum RMSE value of 0.9692 with 14 predictors. The R-squared value continued to improve with more predictors, reaching 0.3327 at the final model, while MAE slightly decreased.

Stepwise regression

set.seed(123)
stepwise_model <- train(
  model_formula, 
  data = training, 
  method = "leapSeq",  # Stepwise Selection en `caret`
  preProc = c("scale", "center"),  # Normaliza los datos
  tuneGrid = expand.grid(nvmax = 4:15),  # Busca entre 4 y 15 variables
  trControl = ctrl
)

# Mostrar resultados
print(stepwise_model)
## Linear Regression with Stepwise Selection 
## 
## 1938 samples
##   14 predictor
## 
## Pre-processing: scaled (14), centered (14) 
## Resampling: Cross-Validated (5 fold, repeated 1 times) 
## Summary of sample sizes: 1551, 1550, 1550, 1550, 1551 
## Resampling results across tuning parameters:
## 
##   nvmax  RMSE       Rsquared   MAE      
##    4     1.0035029  0.2836483  0.7913892
##    5     0.9874094  0.3067943  0.7808447
##    6     1.0073687  0.2777834  0.7984871
##    7     0.9917327  0.3004738  0.7809033
##    8     0.9955014  0.2949272  0.7818203
##    9     0.9937667  0.2978710  0.7823203
##   10     0.9950276  0.2962215  0.7842422
##   11     0.9751242  0.3237965  0.7704189
##   12     0.9699659  0.3321967  0.7657664
##   13     0.9687398  0.3337258  0.7633582
##   14     0.9689263  0.3335756  0.7649670
##   15     0.9689263  0.3335756  0.7649670
## 
## RMSE was used to select the optimal model using the smallest value.
## The final value used for the model was nvmax = 13.
# Graficar RMSE vs. Número de predictores
plot(stepwise_model)

With stepwise regression the optimal model was obtained with 12 predictors, which yielded the lowest RMSE value of 0.9686. The model also showed a steady improvement in R-squared, reaching 0.3333.

Now we will evaluate and compare the performance of three different variable selection methods on our linear regression model. For each model, we make predictions using the testing set and then assess their accuracy.

set.seed(123)
# Creating a DataFrame to store observations and predictions
test_results <- data.frame(observed = testing$average_grade)

# Making predictions
test_results$fw <- predict(forward_model, newdata = testing)
test_results$bw <- predict(backward_model, newdata = testing)
test_results$sw <- predict(stepwise_model, newdata = testing)

# Evaluating each model
metrics_fw <- postResample(pred = test_results$fw, obs = test_results$observed)
metrics_bw <- postResample(pred = test_results$bw, obs = test_results$observed)
metrics_sw <- postResample(pred = test_results$sw, obs = test_results$observed)

# Show metrics
cat("\n🔹 Forward Selection Metrics:\n")
## 
## 🔹 Forward Selection Metrics:
print(metrics_fw)
##      RMSE  Rsquared       MAE 
## 1.0648513 0.2538339 0.8093230
cat("\n🔹 Backward Selection Metrics:\n")
## 
## 🔹 Backward Selection Metrics:
print(metrics_bw)
##      RMSE  Rsquared       MAE 
## 1.0648513 0.2538339 0.8093230
cat("\n🔹 Stepwise Selection Metrics:\n")
## 
## 🔹 Stepwise Selection Metrics:
print(metrics_sw)
##      RMSE  Rsquared       MAE 
## 1.0648513 0.2538339 0.8093230

Forward and Backward selection techniques provide very similar and slightly better performance compared to Stepwise selection, making them more favorable in this case.

Lasso regression

We proceed to apply regularization method techniques, starting with Lasso.

set.seed(123)
# Defining grid
lasso_grid <- expand.grid(fraction = seq(0.01, 1, length = 100))

# Entrenar el modelo Lasso
set.seed(123)
lasso_tune <- train(model_formula, data = training,
                    method = "lasso",
                    preProc = c("scale", "center"), 
                    tuneGrid = lasso_grid,
                    trControl = ctrl)

# Graficar el efecto de lambda en el RMSE
plot(lasso_tune)

# Best lamda
print(lasso_tune$bestTune)
##    fraction
## 98     0.98
# Crear DataFrame para almacenar predicciones y valores reales
test_results <- data.frame(
  observed = testing$average_grade,  # Valores reales
  lasso = predict(lasso_tune, newdata = testing)  # Predicciones del modelo
)

# Evaluar el rendimiento del modelo
metrics_lasso <- postResample(pred = test_results$lasso, obs = test_results$observed)
print(metrics_lasso)
##      RMSE  Rsquared       MAE 
## 1.0634924 0.2550914 0.8084476

The Lasso model with the best lambda value (0.95) improves only very slightly the RMSE and Rsquared compared to models without regularization. In general we are not having good results

Ridge regression

ridge_grid <- expand.grid(lambda = seq(0, .1, length = 100))

# Training Ridge
set.seed(123)
ridge_tune <- train(model_formula, data = training,
                    method = "ridge",
                    preProc = c("scale", "center"), 
                    tuneGrid = ridge_grid,
                    trControl = ctrl)
# Graph
plot(ridge_tune)

# Best lamda
print(ridge_tune$bestTune)
##        lambda
## 11 0.01010101
# DataFrame to store predictions and real values
test_results <- data.frame(
  observed = testing$average_grade,  
  ridge = predict(ridge_tune, newdata = testing))  

# Performance metrics
metrics_ridge <- postResample(pred = test_results$ridge, obs = test_results$observed)
print(metrics_ridge)
##      RMSE  Rsquared       MAE 
## 1.0628071 0.2559616 0.8081206

We obtain almost the same as with Lasso.

Elastic Net regression

elastic_grid <- expand.grid(alpha = seq(0, 1, 0.1), lambda = seq(0, .1, 0.01))

set.seed(123)
elastic_tune <- train(model_formula, data = training,
                     method = "glmnet",
                     preProc = c("scale", "center"),
                     tuneGrid = elastic_grid,
                     trControl = ctrl)

plot(elastic_tune)

print(elastic_tune$bestTune)
##    alpha lambda
## 13   0.1   0.01
test_results <- data.frame(
  observed = testing$average_grade, 
  elastic = predict(elastic_tune, newdata = testing))

metrics_elastic <- postResample(pred = test_results$elastic, 
                                obs = test_results$observed)
print(metrics_elastic)
##      RMSE  Rsquared       MAE 
## 1.0628722 0.2553720 0.8085837

We also have almost the same performance with Elastic Net.

In general, all the models tested have performed moderately, with results indicating a fair amount of prediction error and limited explanatory power, as shown by relatively low R-squared values and RMSE. This could be due to several factors, such as the complexity of the data or the limitations when using traditional statistical models. Moreover, the linear nature of the models might not be capturing all the non-linear relationships within the data.

Machine Learning

We will now transition to machine learning techniques, which are better equipped to handle complex relationships and interactions in the data. These methods may offer improvements in prediction accuracy.

k-Nearest Neighbors (k-NN)

set.seed(123)
# Defining KNN
knn_tune <- train(average_grade ~ ., 
                  data = training,
                  method = "kknn",   
                  preProc = c('scale', 'center'),
                  tuneGrid = data.frame(kmax = c(5, 10, 15, 20), 
                                        distance = 2, kernel = 'optimal'),
                  trControl = ctrl)

# Mostrar los resultados del tuning
print(knn_tune)
## k-Nearest Neighbors 
## 
## 1938 samples
##   41 predictor
## 
## Pre-processing: scaled (41), centered (41) 
## Resampling: Cross-Validated (5 fold, repeated 1 times) 
## Summary of sample sizes: 1551, 1550, 1550, 1550, 1551 
## Resampling results across tuning parameters:
## 
##   kmax  RMSE      Rsquared   MAE      
##    5    1.160551  0.1362891  0.9056258
##   10    1.101026  0.1643669  0.8647512
##   15    1.083114  0.1764108  0.8528798
##   20    1.074406  0.1846833  0.8474628
## 
## Tuning parameter 'distance' was held constant at a value of 2
## Tuning
##  parameter 'kernel' was held constant at a value of optimal
## RMSE was used to select the optimal model using the smallest value.
## The final values used for the model were kmax = 20, distance = 2 and kernel
##  = optimal.
plot(knn_tune)

# Hacer predicciones en el conjunto de prueba
test_results$knn <- predict(knn_tune, testing)

# Evaluar el modelo KNN
knn_metrics <- postResample(pred = test_results$knn, obs = testing$average_grade)
print(knn_metrics)
##      RMSE  Rsquared       MAE 
## 1.1490845 0.1353695 0.8898548

The optimal model was selected with kmax = 20, which means the model considers the average of the 20 nearest neighbors for each prediction. The metrics obtained were the worst up to the moment.

Random Forest

set.seed(123)
# Define the model
rf_tune <- train(average_grade ~ ., 
                 data = training,
                 method = "rf",
                 preProc = c('scale', 'center'),
                 trControl = ctrl,
                 ntree = 100, 
                 tuneGrid = expand.grid(mtry = c(1, 3, 5, 7)),
                 importance = TRUE) 

# Results
print(rf_tune)
## Random Forest 
## 
## 1938 samples
##   41 predictor
## 
## Pre-processing: scaled (41), centered (41) 
## Resampling: Cross-Validated (5 fold, repeated 1 times) 
## Summary of sample sizes: 1551, 1550, 1550, 1550, 1551 
## Resampling results across tuning parameters:
## 
##   mtry  RMSE       Rsquared   MAE      
##   1     1.0929944  0.2905785  0.8726091
##   3     0.9841443  0.3437907  0.7777923
##   5     0.9609172  0.3566022  0.7593463
##   7     0.9538195  0.3607544  0.7525339
## 
## RMSE was used to select the optimal model using the smallest value.
## The final value used for the model was mtry = 7.
plot(rf_tune)

# Predictions on testing set
test_results$rf <- predict(rf_tune, testing)

# Evaluation
rf_metrics <- postResample(pred = test_results$rf, obs = testing$average_grade)
print(rf_metrics)
##      RMSE  Rsquared       MAE 
## 1.0098770 0.3317068 0.7651697
# Visualization
varImpPlot(rf_tune$finalModel)

Random Forest performed better than earlier models, with lower RMSE and higher R-squared. The best model was selected with mtry = 7, meaning the model will consider 7 features at each split of the decision tree. This one appears to be one of the better-performing models so far (RMSE = 1.0133870 and Rsquared = 0.3255387), although it doesn’t predict very well either.

Decision Tree

set.seed(123)
# Defining model
dt_tune <- train(average_grade ~ ., 
                 data = training,
                 method = "rpart",
                 preProc = c('scale', 'center'),
                 tuneGrid = expand.grid(cp = seq(0.001, 0.05, by = 0.005)),
                 trControl = ctrl)

# Results
print(dt_tune)
## CART 
## 
## 1938 samples
##   41 predictor
## 
## Pre-processing: scaled (41), centered (41) 
## Resampling: Cross-Validated (5 fold, repeated 1 times) 
## Summary of sample sizes: 1551, 1550, 1550, 1550, 1551 
## Resampling results across tuning parameters:
## 
##   cp     RMSE      Rsquared   MAE      
##   0.001  1.083498  0.2314922  0.8509588
##   0.006  1.054242  0.2241665  0.8264577
##   0.011  1.049044  0.2214021  0.8276036
##   0.016  1.058506  0.2047494  0.8419989
##   0.021  1.069078  0.1890817  0.8538955
##   0.026  1.078695  0.1752971  0.8614020
##   0.031  1.091076  0.1565998  0.8710403
##   0.036  1.091076  0.1565998  0.8710403
##   0.041  1.106801  0.1314176  0.8843474
##   0.046  1.122416  0.1066643  0.8969738
## 
## RMSE was used to select the optimal model using the smallest value.
## The final value used for the model was cp = 0.011.
plot(dt_tune)

# Predictions
test_results$dt <- predict(dt_tune, testing)

# Evaluation
dt_metrics <- postResample(pred = test_results$dt, obs = testing$average_grade)
print(dt_metrics)
##      RMSE  Rsquared       MAE 
## 1.1218153 0.1720713 0.8738138

The Decision Tree performs worse.

Gradient Boosting

set.seed(123)
# Definir modelo Gradient Boosting
xgb_tune <- train(average_grade ~ ., 
                  data = training,
                  method = "xgbTree",
                  preProc = c('scale', 'center'),
                  trControl = ctrl,
                  tuneGrid = expand.grid(
                    nrounds = c(5, 100),  # Número de árboles PONIA 500, 1000
                    max_depth = c(3, 5, 7),  # Profundidad máxima del árbol
                    eta = c(0.01, 0.1, 0.3),  # Tasa de aprendizaje
                    gamma = c(0, 1, 3),  # Reducción mínima de pérdida
                    colsample_bytree = c(0.8, 1),  # Fracción de características usadas
                    min_child_weight = c(1, 3),  # Peso mínimo de la instancia hija
                    subsample = c(0.8, 1)  # Tasa de muestreo
                  ))
## [19:20:48] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
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## [19:21:05] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:05] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:06] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:06] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:06] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:07] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:07] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:07] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:08] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:08] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:08] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:09] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:09] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:09] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:09] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:10] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:10] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:10] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:11] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:11] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:11] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:12] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:12] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:12] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:12] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:12] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:12] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:13] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:13] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:13] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:13] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:13] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:13] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:13] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:13] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:14] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:14] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:14] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:14] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:14] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:14] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:14] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:15] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:15] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:15] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:15] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:15] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:15] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:15] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:16] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:16] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:16] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:16] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:17] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:17] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:17] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:17] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:17] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:18] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:18] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:18] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:18] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:18] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:19] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:19] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:19] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:19] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:20] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:20] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:20] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:20] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:20] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:21] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:21] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:21] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:22] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:22] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:23] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:23] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:23] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:23] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:24] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:24] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:24] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:25] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:25] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:25] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:26] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:26] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:26] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:27] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:27] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:27] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:27] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:28] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:28] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:28] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:28] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:28] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:29] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:29] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:29] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:29] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:29] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:29] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:29] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:29] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:30] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:30] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:30] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:30] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:30] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:30] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:30] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:30] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:30] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:31] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:31] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:31] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:31] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:31] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:31] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:31] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:31] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:32] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:32] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:32] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:32] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:32] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:32] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:32] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:32] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:33] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:33] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:33] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:33] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:33] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:33] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:33] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:33] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:34] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:34] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:34] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:34] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:34] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:34] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:34] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:34] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:35] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:35] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:35] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:35] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:35] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:35] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:35] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:35] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:36] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:36] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:36] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:36] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:36] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:36] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:37] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:37] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:37] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:37] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:37] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:37] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:37] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:38] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:38] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:38] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:38] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:38] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:38] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:38] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:39] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:39] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:39] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:39] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:39] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:39] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:39] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:40] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:40] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:40] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:40] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:40] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:40] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:40] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:40] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:41] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:41] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:41] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:41] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:41] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:42] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:42] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:42] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:42] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:43] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:43] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:43] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:43] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:43] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:44] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:44] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:44] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:44] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:44] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:45] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:45] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:45] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:45] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:45] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:47] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:47] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:47] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:48] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:48] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:48] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:49] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:49] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:49] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:50] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:50] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:50] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:51] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:51] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:51] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:52] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:52] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:52] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:53] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:53] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:53] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:53] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:54] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:54] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:54] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:54] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:54] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:54] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:54] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:54] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:55] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:55] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:55] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:55] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:55] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:55] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:55] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:55] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:56] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:56] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:56] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:56] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:56] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:56] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:56] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:57] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:57] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:57] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:57] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:57] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:58] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:58] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:58] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:58] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:58] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:59] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:59] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:59] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:21:59] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:00] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:00] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:00] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:00] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:00] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:01] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:01] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:01] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:01] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:01] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:02] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:02] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:02] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:03] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:03] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:03] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:04] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:04] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:04] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:05] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:05] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:05] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:06] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:06] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:06] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:07] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:07] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:07] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:07] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:08] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:08] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:08] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:09] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:09] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:09] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:09] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:09] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:10] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:10] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:10] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:10] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:10] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:10] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:10] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:10] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:10] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:11] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:11] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:11] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:11] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:11] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:11] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:11] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:11] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:11] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:12] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:12] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:12] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:12] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:12] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:12] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:12] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:12] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:13] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:13] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:13] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:13] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:13] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:13] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:13] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:13] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:14] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:14] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:14] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:14] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:14] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:14] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:14] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:14] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:15] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:15] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:15] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:15] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:15] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:15] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:15] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:16] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:16] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:16] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:16] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:16] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:16] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:16] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:16] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:17] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:17] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:17] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:17] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:17] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:17] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:17] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:17] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:18] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:18] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:18] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:18] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:18] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:18] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:18] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:18] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:19] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:19] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:19] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:19] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:19] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:19] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:19] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:20] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:20] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:20] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:20] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:20] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:20] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:21] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:21] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:21] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:21] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:21] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:21] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:21] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:22] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:22] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:22] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:22] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:22] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:23] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:23] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:23] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:23] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:23] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:24] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:24] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:24] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:24] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:24] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:25] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:25] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:25] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:25] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:25] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:26] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:26] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:26] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:26] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:26] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:27] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:27] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:27] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:28] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:28] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:28] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:29] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:29] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:29] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:30] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:30] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:30] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:30] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:31] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:31] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:31] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:32] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:32] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:32] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:33] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:33] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:33] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:33] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:34] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:34] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:34] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:34] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:34] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:34] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:34] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:34] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:35] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:35] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:35] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:35] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:35] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:35] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:36] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:36] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:36] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:36] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:36] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:36] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:36] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:37] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:37] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:37] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:37] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:37] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:37] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:38] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:38] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:38] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:38] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:38] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:39] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:39] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:39] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:39] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:39] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:40] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:40] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:40] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:40] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:41] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:41] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:41] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:41] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:41] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:42] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:42] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:42] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:42] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:43] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:43] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:43] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:44] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:44] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:44] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:45] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:45] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:45] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:47] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:47] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:47] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:47] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:48] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:48] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:48] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:49] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:49] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:49] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:49] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:50] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:50] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:50] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:50] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:50] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:50] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:50] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:50] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:51] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:51] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:51] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:51] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:51] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:51] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:51] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:51] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:51] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:52] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:52] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:52] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:52] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:52] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:52] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:52] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:52] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:52] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:53] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:53] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:53] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:53] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:53] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:53] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:53] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:53] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:54] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:54] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:54] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:54] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:54] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:54] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:54] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:54] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:55] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:55] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:55] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:55] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:55] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:55] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:55] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:55] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:56] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:56] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:56] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:56] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:56] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:56] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:56] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:56] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:57] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:57] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:57] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:57] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:57] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:57] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:57] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:57] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:58] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:58] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:58] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:58] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:58] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:58] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:58] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:58] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:59] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:59] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:59] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:59] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:59] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:22:59] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:00] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:00] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:00] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:00] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:00] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:00] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:00] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:01] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:01] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:01] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:01] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:01] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:01] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:01] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:01] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:02] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:02] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:02] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:02] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:02] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:03] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:03] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:03] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:03] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:04] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:04] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:04] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:04] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:04] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:05] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:05] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:05] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:05] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:05] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:06] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:06] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:06] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:06] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:06] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:07] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:07] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:07] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:08] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:08] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:08] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:09] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:09] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:09] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:10] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:10] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:10] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:11] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:11] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:11] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:11] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:12] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:12] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:12] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:13] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:13] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:13] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:14] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:14] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:14] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:14] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:14] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:14] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:15] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:15] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:15] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:15] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:15] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:15] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:15] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:15] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:16] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:16] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:16] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:16] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:16] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:16] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:16] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:17] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:17] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:17] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:17] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:17] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:17] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:18] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:18] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:18] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:18] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:18] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:19] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:19] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:19] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:19] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:20] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:20] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:20] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:20] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:20] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:21] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:21] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:21] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:21] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:22] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:22] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:22] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:22] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:23] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:23] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:24] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:24] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:24] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:25] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:25] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:26] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:26] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:26] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:27] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:27] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:28] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:28] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:28] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:29] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:29] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:29] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:30] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:30] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:30] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:31] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:31] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:31] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:32] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:32] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:32] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:32] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:32] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:32] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:33] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:33] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:33] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:33] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:33] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:33] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:33] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:33] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:34] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:34] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:34] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:34] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:34] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:34] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:34] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:35] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:35] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:35] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:35] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:35] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:35] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:35] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:35] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:36] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:36] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:36] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:36] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:36] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:36] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:36] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:37] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:37] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:37] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:37] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:37] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:37] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:37] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:38] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:38] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:38] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:38] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:38] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:38] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:38] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:38] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:39] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:39] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:39] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:39] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:39] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:39] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:39] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:40] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:40] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:40] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:40] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:40] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:40] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:41] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:41] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:41] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:41] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:41] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:41] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:41] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:42] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:42] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:42] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:42] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:42] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:42] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:42] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:43] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:43] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:43] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:43] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:43] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:43] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:43] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:43] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:44] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:44] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:44] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:44] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:44] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:44] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:45] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:45] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:45] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:45] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:45] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:45] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:47] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:47] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:47] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:47] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:48] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:48] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:48] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:49] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:49] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:49] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:49] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:50] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:50] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:50] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:50] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:51] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:51] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:51] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:51] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:52] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:52] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:53] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:53] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:53] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:54] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:54] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:55] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:55] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:55] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:56] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:56] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:56] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:57] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:57] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:58] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:58] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:58] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:59] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:23:59] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:24:00] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:24:00] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:24:00] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:24:00] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:24:01] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:24:01] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:24:01] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:24:01] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:24:01] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:24:01] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:24:01] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:24:02] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:24:02] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:24:02] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:24:02] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:24:03] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:24:03] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:24:03] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:24:03] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:24:03] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:24:04] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:24:04] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:24:04] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:24:04] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:24:05] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:24:05] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:24:06] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:24:06] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:24:07] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:24:07] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:24:08] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:24:09] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:24:09] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:24:10] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:24:10] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:24:10] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:24:11] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:24:11] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:24:11] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:24:12] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:24:12] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:24:13] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:24:13] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:24:13] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:24:14] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:24:14] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:24:14] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:24:15] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:24:15] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:24:15] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:24:15] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:24:16] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:24:16] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:24:17] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:24:17] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:24:18] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:24:18] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:24:18] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:24:19] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:24:19] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:24:20] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:24:20] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:24:20] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:24:21] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:24:21] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:24:22] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:24:22] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:24:22] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:24:23] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:24:23] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:24:23] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:24:24] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:24:24] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:24:25] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## [19:24:25] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
## Warning in nominalTrainWorkflow(x = x, y = y, wts = weights, info = trainInfo,
## : There were missing values in resampled performance measures.
# Mostrar resultados del tuning
print(xgb_tune)
## eXtreme Gradient Boosting 
## 
## 1938 samples
##   41 predictor
## 
## Pre-processing: scaled (41), centered (41) 
## Resampling: Cross-Validated (5 fold, repeated 1 times) 
## Summary of sample sizes: 1551, 1550, 1550, 1550, 1551 
## Resampling results across tuning parameters:
## 
##   eta   max_depth  gamma  colsample_bytree  min_child_weight  subsample
##   0.01  3          0      0.8               1                 0.8      
##   0.01  3          0      0.8               1                 0.8      
##   0.01  3          0      0.8               1                 1.0      
##   0.01  3          0      0.8               1                 1.0      
##   0.01  3          0      0.8               3                 0.8      
##   0.01  3          0      0.8               3                 0.8      
##   0.01  3          0      0.8               3                 1.0      
##   0.01  3          0      0.8               3                 1.0      
##   0.01  3          0      1.0               1                 0.8      
##   0.01  3          0      1.0               1                 0.8      
##   0.01  3          0      1.0               1                 1.0      
##   0.01  3          0      1.0               1                 1.0      
##   0.01  3          0      1.0               3                 0.8      
##   0.01  3          0      1.0               3                 0.8      
##   0.01  3          0      1.0               3                 1.0      
##   0.01  3          0      1.0               3                 1.0      
##   0.01  3          1      0.8               1                 0.8      
##   0.01  3          1      0.8               1                 0.8      
##   0.01  3          1      0.8               1                 1.0      
##   0.01  3          1      0.8               1                 1.0      
##   0.01  3          1      0.8               3                 0.8      
##   0.01  3          1      0.8               3                 0.8      
##   0.01  3          1      0.8               3                 1.0      
##   0.01  3          1      0.8               3                 1.0      
##   0.01  3          1      1.0               1                 0.8      
##   0.01  3          1      1.0               1                 0.8      
##   0.01  3          1      1.0               1                 1.0      
##   0.01  3          1      1.0               1                 1.0      
##   0.01  3          1      1.0               3                 0.8      
##   0.01  3          1      1.0               3                 0.8      
##   0.01  3          1      1.0               3                 1.0      
##   0.01  3          1      1.0               3                 1.0      
##   0.01  3          3      0.8               1                 0.8      
##   0.01  3          3      0.8               1                 0.8      
##   0.01  3          3      0.8               1                 1.0      
##   0.01  3          3      0.8               1                 1.0      
##   0.01  3          3      0.8               3                 0.8      
##   0.01  3          3      0.8               3                 0.8      
##   0.01  3          3      0.8               3                 1.0      
##   0.01  3          3      0.8               3                 1.0      
##   0.01  3          3      1.0               1                 0.8      
##   0.01  3          3      1.0               1                 0.8      
##   0.01  3          3      1.0               1                 1.0      
##   0.01  3          3      1.0               1                 1.0      
##   0.01  3          3      1.0               3                 0.8      
##   0.01  3          3      1.0               3                 0.8      
##   0.01  3          3      1.0               3                 1.0      
##   0.01  3          3      1.0               3                 1.0      
##   0.01  5          0      0.8               1                 0.8      
##   0.01  5          0      0.8               1                 0.8      
##   0.01  5          0      0.8               1                 1.0      
##   0.01  5          0      0.8               1                 1.0      
##   0.01  5          0      0.8               3                 0.8      
##   0.01  5          0      0.8               3                 0.8      
##   0.01  5          0      0.8               3                 1.0      
##   0.01  5          0      0.8               3                 1.0      
##   0.01  5          0      1.0               1                 0.8      
##   0.01  5          0      1.0               1                 0.8      
##   0.01  5          0      1.0               1                 1.0      
##   0.01  5          0      1.0               1                 1.0      
##   0.01  5          0      1.0               3                 0.8      
##   0.01  5          0      1.0               3                 0.8      
##   0.01  5          0      1.0               3                 1.0      
##   0.01  5          0      1.0               3                 1.0      
##   0.01  5          1      0.8               1                 0.8      
##   0.01  5          1      0.8               1                 0.8      
##   0.01  5          1      0.8               1                 1.0      
##   0.01  5          1      0.8               1                 1.0      
##   0.01  5          1      0.8               3                 0.8      
##   0.01  5          1      0.8               3                 0.8      
##   0.01  5          1      0.8               3                 1.0      
##   0.01  5          1      0.8               3                 1.0      
##   0.01  5          1      1.0               1                 0.8      
##   0.01  5          1      1.0               1                 0.8      
##   0.01  5          1      1.0               1                 1.0      
##   0.01  5          1      1.0               1                 1.0      
##   0.01  5          1      1.0               3                 0.8      
##   0.01  5          1      1.0               3                 0.8      
##   0.01  5          1      1.0               3                 1.0      
##   0.01  5          1      1.0               3                 1.0      
##   0.01  5          3      0.8               1                 0.8      
##   0.01  5          3      0.8               1                 0.8      
##   0.01  5          3      0.8               1                 1.0      
##   0.01  5          3      0.8               1                 1.0      
##   0.01  5          3      0.8               3                 0.8      
##   0.01  5          3      0.8               3                 0.8      
##   0.01  5          3      0.8               3                 1.0      
##   0.01  5          3      0.8               3                 1.0      
##   0.01  5          3      1.0               1                 0.8      
##   0.01  5          3      1.0               1                 0.8      
##   0.01  5          3      1.0               1                 1.0      
##   0.01  5          3      1.0               1                 1.0      
##   0.01  5          3      1.0               3                 0.8      
##   0.01  5          3      1.0               3                 0.8      
##   0.01  5          3      1.0               3                 1.0      
##   0.01  5          3      1.0               3                 1.0      
##   0.01  7          0      0.8               1                 0.8      
##   0.01  7          0      0.8               1                 0.8      
##   0.01  7          0      0.8               1                 1.0      
##   0.01  7          0      0.8               1                 1.0      
##   0.01  7          0      0.8               3                 0.8      
##   0.01  7          0      0.8               3                 0.8      
##   0.01  7          0      0.8               3                 1.0      
##   0.01  7          0      0.8               3                 1.0      
##   0.01  7          0      1.0               1                 0.8      
##   0.01  7          0      1.0               1                 0.8      
##   0.01  7          0      1.0               1                 1.0      
##   0.01  7          0      1.0               1                 1.0      
##   0.01  7          0      1.0               3                 0.8      
##   0.01  7          0      1.0               3                 0.8      
##   0.01  7          0      1.0               3                 1.0      
##   0.01  7          0      1.0               3                 1.0      
##   0.01  7          1      0.8               1                 0.8      
##   0.01  7          1      0.8               1                 0.8      
##   0.01  7          1      0.8               1                 1.0      
##   0.01  7          1      0.8               1                 1.0      
##   0.01  7          1      0.8               3                 0.8      
##   0.01  7          1      0.8               3                 0.8      
##   0.01  7          1      0.8               3                 1.0      
##   0.01  7          1      0.8               3                 1.0      
##   0.01  7          1      1.0               1                 0.8      
##   0.01  7          1      1.0               1                 0.8      
##   0.01  7          1      1.0               1                 1.0      
##   0.01  7          1      1.0               1                 1.0      
##   0.01  7          1      1.0               3                 0.8      
##   0.01  7          1      1.0               3                 0.8      
##   0.01  7          1      1.0               3                 1.0      
##   0.01  7          1      1.0               3                 1.0      
##   0.01  7          3      0.8               1                 0.8      
##   0.01  7          3      0.8               1                 0.8      
##   0.01  7          3      0.8               1                 1.0      
##   0.01  7          3      0.8               1                 1.0      
##   0.01  7          3      0.8               3                 0.8      
##   0.01  7          3      0.8               3                 0.8      
##   0.01  7          3      0.8               3                 1.0      
##   0.01  7          3      0.8               3                 1.0      
##   0.01  7          3      1.0               1                 0.8      
##   0.01  7          3      1.0               1                 0.8      
##   0.01  7          3      1.0               1                 1.0      
##   0.01  7          3      1.0               1                 1.0      
##   0.01  7          3      1.0               3                 0.8      
##   0.01  7          3      1.0               3                 0.8      
##   0.01  7          3      1.0               3                 1.0      
##   0.01  7          3      1.0               3                 1.0      
##   0.10  3          0      0.8               1                 0.8      
##   0.10  3          0      0.8               1                 0.8      
##   0.10  3          0      0.8               1                 1.0      
##   0.10  3          0      0.8               1                 1.0      
##   0.10  3          0      0.8               3                 0.8      
##   0.10  3          0      0.8               3                 0.8      
##   0.10  3          0      0.8               3                 1.0      
##   0.10  3          0      0.8               3                 1.0      
##   0.10  3          0      1.0               1                 0.8      
##   0.10  3          0      1.0               1                 0.8      
##   0.10  3          0      1.0               1                 1.0      
##   0.10  3          0      1.0               1                 1.0      
##   0.10  3          0      1.0               3                 0.8      
##   0.10  3          0      1.0               3                 0.8      
##   0.10  3          0      1.0               3                 1.0      
##   0.10  3          0      1.0               3                 1.0      
##   0.10  3          1      0.8               1                 0.8      
##   0.10  3          1      0.8               1                 0.8      
##   0.10  3          1      0.8               1                 1.0      
##   0.10  3          1      0.8               1                 1.0      
##   0.10  3          1      0.8               3                 0.8      
##   0.10  3          1      0.8               3                 0.8      
##   0.10  3          1      0.8               3                 1.0      
##   0.10  3          1      0.8               3                 1.0      
##   0.10  3          1      1.0               1                 0.8      
##   0.10  3          1      1.0               1                 0.8      
##   0.10  3          1      1.0               1                 1.0      
##   0.10  3          1      1.0               1                 1.0      
##   0.10  3          1      1.0               3                 0.8      
##   0.10  3          1      1.0               3                 0.8      
##   0.10  3          1      1.0               3                 1.0      
##   0.10  3          1      1.0               3                 1.0      
##   0.10  3          3      0.8               1                 0.8      
##   0.10  3          3      0.8               1                 0.8      
##   0.10  3          3      0.8               1                 1.0      
##   0.10  3          3      0.8               1                 1.0      
##   0.10  3          3      0.8               3                 0.8      
##   0.10  3          3      0.8               3                 0.8      
##   0.10  3          3      0.8               3                 1.0      
##   0.10  3          3      0.8               3                 1.0      
##   0.10  3          3      1.0               1                 0.8      
##   0.10  3          3      1.0               1                 0.8      
##   0.10  3          3      1.0               1                 1.0      
##   0.10  3          3      1.0               1                 1.0      
##   0.10  3          3      1.0               3                 0.8      
##   0.10  3          3      1.0               3                 0.8      
##   0.10  3          3      1.0               3                 1.0      
##   0.10  3          3      1.0               3                 1.0      
##   0.10  5          0      0.8               1                 0.8      
##   0.10  5          0      0.8               1                 0.8      
##   0.10  5          0      0.8               1                 1.0      
##   0.10  5          0      0.8               1                 1.0      
##   0.10  5          0      0.8               3                 0.8      
##   0.10  5          0      0.8               3                 0.8      
##   0.10  5          0      0.8               3                 1.0      
##   0.10  5          0      0.8               3                 1.0      
##   0.10  5          0      1.0               1                 0.8      
##   0.10  5          0      1.0               1                 0.8      
##   0.10  5          0      1.0               1                 1.0      
##   0.10  5          0      1.0               1                 1.0      
##   0.10  5          0      1.0               3                 0.8      
##   0.10  5          0      1.0               3                 0.8      
##   0.10  5          0      1.0               3                 1.0      
##   0.10  5          0      1.0               3                 1.0      
##   0.10  5          1      0.8               1                 0.8      
##   0.10  5          1      0.8               1                 0.8      
##   0.10  5          1      0.8               1                 1.0      
##   0.10  5          1      0.8               1                 1.0      
##   0.10  5          1      0.8               3                 0.8      
##   0.10  5          1      0.8               3                 0.8      
##   0.10  5          1      0.8               3                 1.0      
##   0.10  5          1      0.8               3                 1.0      
##   0.10  5          1      1.0               1                 0.8      
##   0.10  5          1      1.0               1                 0.8      
##   0.10  5          1      1.0               1                 1.0      
##   0.10  5          1      1.0               1                 1.0      
##   0.10  5          1      1.0               3                 0.8      
##   0.10  5          1      1.0               3                 0.8      
##   0.10  5          1      1.0               3                 1.0      
##   0.10  5          1      1.0               3                 1.0      
##   0.10  5          3      0.8               1                 0.8      
##   0.10  5          3      0.8               1                 0.8      
##   0.10  5          3      0.8               1                 1.0      
##   0.10  5          3      0.8               1                 1.0      
##   0.10  5          3      0.8               3                 0.8      
##   0.10  5          3      0.8               3                 0.8      
##   0.10  5          3      0.8               3                 1.0      
##   0.10  5          3      0.8               3                 1.0      
##   0.10  5          3      1.0               1                 0.8      
##   0.10  5          3      1.0               1                 0.8      
##   0.10  5          3      1.0               1                 1.0      
##   0.10  5          3      1.0               1                 1.0      
##   0.10  5          3      1.0               3                 0.8      
##   0.10  5          3      1.0               3                 0.8      
##   0.10  5          3      1.0               3                 1.0      
##   0.10  5          3      1.0               3                 1.0      
##   0.10  7          0      0.8               1                 0.8      
##   0.10  7          0      0.8               1                 0.8      
##   0.10  7          0      0.8               1                 1.0      
##   0.10  7          0      0.8               1                 1.0      
##   0.10  7          0      0.8               3                 0.8      
##   0.10  7          0      0.8               3                 0.8      
##   0.10  7          0      0.8               3                 1.0      
##   0.10  7          0      0.8               3                 1.0      
##   0.10  7          0      1.0               1                 0.8      
##   0.10  7          0      1.0               1                 0.8      
##   0.10  7          0      1.0               1                 1.0      
##   0.10  7          0      1.0               1                 1.0      
##   0.10  7          0      1.0               3                 0.8      
##   0.10  7          0      1.0               3                 0.8      
##   0.10  7          0      1.0               3                 1.0      
##   0.10  7          0      1.0               3                 1.0      
##   0.10  7          1      0.8               1                 0.8      
##   0.10  7          1      0.8               1                 0.8      
##   0.10  7          1      0.8               1                 1.0      
##   0.10  7          1      0.8               1                 1.0      
##   0.10  7          1      0.8               3                 0.8      
##   0.10  7          1      0.8               3                 0.8      
##   0.10  7          1      0.8               3                 1.0      
##   0.10  7          1      0.8               3                 1.0      
##   0.10  7          1      1.0               1                 0.8      
##   0.10  7          1      1.0               1                 0.8      
##   0.10  7          1      1.0               1                 1.0      
##   0.10  7          1      1.0               1                 1.0      
##   0.10  7          1      1.0               3                 0.8      
##   0.10  7          1      1.0               3                 0.8      
##   0.10  7          1      1.0               3                 1.0      
##   0.10  7          1      1.0               3                 1.0      
##   0.10  7          3      0.8               1                 0.8      
##   0.10  7          3      0.8               1                 0.8      
##   0.10  7          3      0.8               1                 1.0      
##   0.10  7          3      0.8               1                 1.0      
##   0.10  7          3      0.8               3                 0.8      
##   0.10  7          3      0.8               3                 0.8      
##   0.10  7          3      0.8               3                 1.0      
##   0.10  7          3      0.8               3                 1.0      
##   0.10  7          3      1.0               1                 0.8      
##   0.10  7          3      1.0               1                 0.8      
##   0.10  7          3      1.0               1                 1.0      
##   0.10  7          3      1.0               1                 1.0      
##   0.10  7          3      1.0               3                 0.8      
##   0.10  7          3      1.0               3                 0.8      
##   0.10  7          3      1.0               3                 1.0      
##   0.10  7          3      1.0               3                 1.0      
##   0.30  3          0      0.8               1                 0.8      
##   0.30  3          0      0.8               1                 0.8      
##   0.30  3          0      0.8               1                 1.0      
##   0.30  3          0      0.8               1                 1.0      
##   0.30  3          0      0.8               3                 0.8      
##   0.30  3          0      0.8               3                 0.8      
##   0.30  3          0      0.8               3                 1.0      
##   0.30  3          0      0.8               3                 1.0      
##   0.30  3          0      1.0               1                 0.8      
##   0.30  3          0      1.0               1                 0.8      
##   0.30  3          0      1.0               1                 1.0      
##   0.30  3          0      1.0               1                 1.0      
##   0.30  3          0      1.0               3                 0.8      
##   0.30  3          0      1.0               3                 0.8      
##   0.30  3          0      1.0               3                 1.0      
##   0.30  3          0      1.0               3                 1.0      
##   0.30  3          1      0.8               1                 0.8      
##   0.30  3          1      0.8               1                 0.8      
##   0.30  3          1      0.8               1                 1.0      
##   0.30  3          1      0.8               1                 1.0      
##   0.30  3          1      0.8               3                 0.8      
##   0.30  3          1      0.8               3                 0.8      
##   0.30  3          1      0.8               3                 1.0      
##   0.30  3          1      0.8               3                 1.0      
##   0.30  3          1      1.0               1                 0.8      
##   0.30  3          1      1.0               1                 0.8      
##   0.30  3          1      1.0               1                 1.0      
##   0.30  3          1      1.0               1                 1.0      
##   0.30  3          1      1.0               3                 0.8      
##   0.30  3          1      1.0               3                 0.8      
##   0.30  3          1      1.0               3                 1.0      
##   0.30  3          1      1.0               3                 1.0      
##   0.30  3          3      0.8               1                 0.8      
##   0.30  3          3      0.8               1                 0.8      
##   0.30  3          3      0.8               1                 1.0      
##   0.30  3          3      0.8               1                 1.0      
##   0.30  3          3      0.8               3                 0.8      
##   0.30  3          3      0.8               3                 0.8      
##   0.30  3          3      0.8               3                 1.0      
##   0.30  3          3      0.8               3                 1.0      
##   0.30  3          3      1.0               1                 0.8      
##   0.30  3          3      1.0               1                 0.8      
##   0.30  3          3      1.0               1                 1.0      
##   0.30  3          3      1.0               1                 1.0      
##   0.30  3          3      1.0               3                 0.8      
##   0.30  3          3      1.0               3                 0.8      
##   0.30  3          3      1.0               3                 1.0      
##   0.30  3          3      1.0               3                 1.0      
##   0.30  5          0      0.8               1                 0.8      
##   0.30  5          0      0.8               1                 0.8      
##   0.30  5          0      0.8               1                 1.0      
##   0.30  5          0      0.8               1                 1.0      
##   0.30  5          0      0.8               3                 0.8      
##   0.30  5          0      0.8               3                 0.8      
##   0.30  5          0      0.8               3                 1.0      
##   0.30  5          0      0.8               3                 1.0      
##   0.30  5          0      1.0               1                 0.8      
##   0.30  5          0      1.0               1                 0.8      
##   0.30  5          0      1.0               1                 1.0      
##   0.30  5          0      1.0               1                 1.0      
##   0.30  5          0      1.0               3                 0.8      
##   0.30  5          0      1.0               3                 0.8      
##   0.30  5          0      1.0               3                 1.0      
##   0.30  5          0      1.0               3                 1.0      
##   0.30  5          1      0.8               1                 0.8      
##   0.30  5          1      0.8               1                 0.8      
##   0.30  5          1      0.8               1                 1.0      
##   0.30  5          1      0.8               1                 1.0      
##   0.30  5          1      0.8               3                 0.8      
##   0.30  5          1      0.8               3                 0.8      
##   0.30  5          1      0.8               3                 1.0      
##   0.30  5          1      0.8               3                 1.0      
##   0.30  5          1      1.0               1                 0.8      
##   0.30  5          1      1.0               1                 0.8      
##   0.30  5          1      1.0               1                 1.0      
##   0.30  5          1      1.0               1                 1.0      
##   0.30  5          1      1.0               3                 0.8      
##   0.30  5          1      1.0               3                 0.8      
##   0.30  5          1      1.0               3                 1.0      
##   0.30  5          1      1.0               3                 1.0      
##   0.30  5          3      0.8               1                 0.8      
##   0.30  5          3      0.8               1                 0.8      
##   0.30  5          3      0.8               1                 1.0      
##   0.30  5          3      0.8               1                 1.0      
##   0.30  5          3      0.8               3                 0.8      
##   0.30  5          3      0.8               3                 0.8      
##   0.30  5          3      0.8               3                 1.0      
##   0.30  5          3      0.8               3                 1.0      
##   0.30  5          3      1.0               1                 0.8      
##   0.30  5          3      1.0               1                 0.8      
##   0.30  5          3      1.0               1                 1.0      
##   0.30  5          3      1.0               1                 1.0      
##   0.30  5          3      1.0               3                 0.8      
##   0.30  5          3      1.0               3                 0.8      
##   0.30  5          3      1.0               3                 1.0      
##   0.30  5          3      1.0               3                 1.0      
##   0.30  7          0      0.8               1                 0.8      
##   0.30  7          0      0.8               1                 0.8      
##   0.30  7          0      0.8               1                 1.0      
##   0.30  7          0      0.8               1                 1.0      
##   0.30  7          0      0.8               3                 0.8      
##   0.30  7          0      0.8               3                 0.8      
##   0.30  7          0      0.8               3                 1.0      
##   0.30  7          0      0.8               3                 1.0      
##   0.30  7          0      1.0               1                 0.8      
##   0.30  7          0      1.0               1                 0.8      
##   0.30  7          0      1.0               1                 1.0      
##   0.30  7          0      1.0               1                 1.0      
##   0.30  7          0      1.0               3                 0.8      
##   0.30  7          0      1.0               3                 0.8      
##   0.30  7          0      1.0               3                 1.0      
##   0.30  7          0      1.0               3                 1.0      
##   0.30  7          1      0.8               1                 0.8      
##   0.30  7          1      0.8               1                 0.8      
##   0.30  7          1      0.8               1                 1.0      
##   0.30  7          1      0.8               1                 1.0      
##   0.30  7          1      0.8               3                 0.8      
##   0.30  7          1      0.8               3                 0.8      
##   0.30  7          1      0.8               3                 1.0      
##   0.30  7          1      0.8               3                 1.0      
##   0.30  7          1      1.0               1                 0.8      
##   0.30  7          1      1.0               1                 0.8      
##   0.30  7          1      1.0               1                 1.0      
##   0.30  7          1      1.0               1                 1.0      
##   0.30  7          1      1.0               3                 0.8      
##   0.30  7          1      1.0               3                 0.8      
##   0.30  7          1      1.0               3                 1.0      
##   0.30  7          1      1.0               3                 1.0      
##   0.30  7          3      0.8               1                 0.8      
##   0.30  7          3      0.8               1                 0.8      
##   0.30  7          3      0.8               1                 1.0      
##   0.30  7          3      0.8               1                 1.0      
##   0.30  7          3      0.8               3                 0.8      
##   0.30  7          3      0.8               3                 0.8      
##   0.30  7          3      0.8               3                 1.0      
##   0.30  7          3      0.8               3                 1.0      
##   0.30  7          3      1.0               1                 0.8      
##   0.30  7          3      1.0               1                 0.8      
##   0.30  7          3      1.0               1                 1.0      
##   0.30  7          3      1.0               1                 1.0      
##   0.30  7          3      1.0               3                 0.8      
##   0.30  7          3      1.0               3                 0.8      
##   0.30  7          3      1.0               3                 1.0      
##   0.30  7          3      1.0               3                 1.0      
##   nrounds  RMSE        Rsquared    MAE       
##     5      11.7494980  0.07740434  11.6897893
##   100       4.6391546  0.27321785   4.5107240
##     5      11.7493499  0.11081278  11.6899118
##   100       4.6368254  0.27234426   4.5101832
##     5      11.7492618  0.13117190  11.6896857
##   100       4.6391525  0.27945962   4.5110111
##     5      11.7494463  0.12685507  11.6900251
##   100       4.6366073  0.27481847   4.5100895
##     5      11.7498127  0.09137458  11.6902094
##   100       4.6390568  0.27381897   4.5118356
##     5      11.7493992  0.08994993  11.6899999
##   100       4.6364097  0.26967898   4.5107000
##     5      11.7498180  0.13544792  11.6902472
##   100       4.6374943  0.27969096   4.5104854
##     5      11.7493992  0.08994993  11.6899999
##   100       4.6357726  0.27261341   4.5101659
##     5      11.7496676  0.10211559  11.6900190
##   100       4.6389340  0.27549264   4.5105117
##     5      11.7495147  0.13060085  11.6900794
##   100       4.6371558  0.26964904   4.5101506
##     5      11.7498325  0.10304278  11.6901709
##   100       4.6396271  0.27599296   4.5109880
##     5      11.7494463  0.13448942  11.6900585
##   100       4.6366694  0.27201715   4.5096876
##     5      11.7494382  0.09953124  11.6898461
##   100       4.6395538  0.27212687   4.5122736
##     5      11.7493992  0.08994993  11.6899999
##   100       4.6364360  0.26909136   4.5105650
##     5      11.7495356  0.09419323  11.6899330
##   100       4.6382914  0.27703210   4.5109506
##     5      11.7493992  0.08994993  11.6899999
##   100       4.6358249  0.27211118   4.5100672
##     5      11.7495982  0.07654492  11.6899085
##   100       4.6386636  0.27198338   4.5095787
##     5      11.7494500  0.10320043  11.6899909
##   100       4.6371165  0.27001446   4.5098623
##     5      11.7498019  0.11405277  11.6901244
##   100       4.6387913  0.27618439   4.5099098
##     5      11.7492666  0.11654898  11.6898160
##   100       4.6362097  0.27386787   4.5091288
##     5      11.7498876  0.07587369  11.6902199
##   100       4.6385693  0.27305280   4.5106146
##     5      11.7493992  0.08994993  11.6899999
##   100       4.6362478  0.26922823   4.5100876
##     5      11.7494203  0.10392826  11.6896953
##   100       4.6377611  0.27277424   4.5098218
##     5      11.7493992  0.08994993  11.6899999
##   100       4.6358995  0.27135231   4.5098144
##     5      11.7499828  0.10637016  11.6903312
##   100       4.6399397  0.27555881   4.5118140
##     5      11.7493184  0.10411394  11.6898623
##   100       4.6368601  0.27799070   4.5109088
##     5      11.7497730  0.09489406  11.6900871
##   100       4.6395841  0.27718576   4.5111724
##     5      11.7493562  0.11274434  11.6899414
##   100       4.6366521  0.27668316   4.5105799
##     5      11.7493139  0.09691938  11.6897174
##   100       4.6383685  0.27514434   4.5113320
##     5      11.7493992  0.08994993  11.6899999
##   100       4.6362089  0.27283317   4.5110799
##     5      11.7499105  0.14510727  11.6903340
##   100       4.6380728  0.27987349   4.5111270
##     5      11.7493992  0.08994993  11.6899999
##   100       4.6357706  0.27637044   4.5108100
##     5      11.7496863  0.10510983  11.6899972
##   100       4.6391088  0.27541604   4.5107071
##     5      11.7494205  0.09385794  11.6899780
##   100       4.6368517  0.27051649   4.5102521
##     5      11.7495528  0.10960676  11.6899065
##   100       4.6390093  0.28356292   4.5110209
##     5      11.7493650  0.12257786  11.6899378
##   100       4.6361225  0.27911151   4.5100819
##     5      11.7493352  0.11496835  11.6897359
##   100       4.6383733  0.27776977   4.5113992
##     5      11.7493992  0.08994993  11.6899999
##   100       4.6361374  0.27328229   4.5108747
##     5      11.7495895  0.15485412  11.6900951
##   100       4.6382242  0.27732494   4.5111866
##     5      11.7493992  0.08994993  11.6899999
##   100       4.6356159  0.27624754   4.5104525
##     5      11.7496487  0.10692271  11.6900170
##   100       4.6406929  0.27415751   4.5119688
##     5      11.7493373  0.11646885  11.6898989
##   100       4.6368828  0.27160861   4.5097915
##     5      11.7495731  0.10105215  11.6899232
##   100       4.6392570  0.27819199   4.5103619
##     5      11.7491502  0.12112250  11.6897334
##   100       4.6362368  0.27547642   4.5095692
##     5      11.7495424  0.13531362  11.6898731
##   100       4.6379391  0.27611479   4.5102997
##     5      11.7493992  0.08994993  11.6899999
##   100       4.6358597  0.27222763   4.5102054
##     5      11.7495966  0.11659344  11.6899678
##   100       4.6383735  0.27339279   4.5106603
##     5      11.7493992  0.08994993  11.6899999
##   100       4.6354985  0.27435554   4.5099298
##     5      11.7496026  0.11704812  11.6899687
##   100       4.6402064  0.27746043   4.5120903
##     5      11.7493946  0.11264406  11.6899457
##   100       4.6368216  0.27698793   4.5108720
##     5      11.7496256  0.15749470  11.6900743
##   100       4.6386279  0.27889155   4.5103544
##     5      11.7492094  0.14706646  11.6897695
##   100       4.6367005  0.27701856   4.5104124
##     5      11.7496864  0.10700205  11.6900642
##   100       4.6387113  0.27472003   4.5116603
##     5      11.7493992  0.08994993  11.6899999
##   100       4.6362061  0.27283431   4.5110772
##     5      11.7498029  0.08587727  11.6902751
##   100       4.6381138  0.27992180   4.5113861
##     5      11.7493992  0.08994993  11.6899999
##   100       4.6357706  0.27637044   4.5108100
##     5      11.7496605  0.11896619  11.6900612
##   100       4.6396521  0.27007720   4.5110915
##     5      11.7494736  0.11602671  11.6900677
##   100       4.6362365  0.27344729   4.5097468
##     5      11.7494910  0.11611858  11.6898296
##   100       4.6388157  0.27901012   4.5103810
##     5      11.7494997  0.11115484  11.6900829
##   100       4.6365128  0.27639391   4.5102030
##     5      11.7495285  0.12251399  11.6898603
##   100       4.6387737  0.27206906   4.5114699
##     5      11.7493992  0.08994993  11.6899999
##   100       4.6361137  0.27332479   4.5108524
##     5      11.7495533  0.10083991  11.6899681
##   100       4.6387154  0.28026005   4.5116132
##     5      11.7493992  0.08994993  11.6899999
##   100       4.6356159  0.27624754   4.5104525
##     5      11.7500008  0.09154627  11.6903256
##   100       4.6393481  0.27190259   4.5105454
##     5      11.7494970  0.12283614  11.6901096
##   100       4.6364893  0.27221005   4.5097306
##     5      11.7495931  0.09667144  11.6898969
##   100       4.6391885  0.27683102   4.5103669
##     5      11.7493037  0.11876822  11.6898698
##   100       4.6360350  0.27519746   4.5092535
##     5      11.7500128  0.09349326  11.6903659
##   100       4.6381398  0.27275593   4.5105728
##     5      11.7493992  0.08994993  11.6899999
##   100       4.6358597  0.27222763   4.5102054
##     5      11.7496328  0.08223125  11.6899643
##   100       4.6377253  0.27604530   4.5101962
##     5      11.7493992  0.08994993  11.6899999
##   100       4.6354985  0.27435554   4.5099298
##     5       7.3528374  0.20482389   7.2641155
##   100       0.9428047  0.36787976   0.7422379
##     5       7.3533656  0.22544101   7.2660520
##   100       0.9486601  0.36084171   0.7457819
##     5       7.3550445  0.18672911   7.2647930
##   100       0.9454164  0.36523323   0.7426580
##     5       7.3518869  0.22072257   7.2647269
##   100       0.9429419  0.36886330   0.7435243
##     5       7.3531573  0.21115735   7.2645612
##   100       0.9434531  0.36868051   0.7416736
##     5       7.3517823  0.23253250   7.2652772
##   100       0.9473240  0.36286695   0.7466159
##     5       7.3544485  0.23060536   7.2664198
##   100       0.9465499  0.36391637   0.7452077
##     5       7.3514828  0.23816839   7.2650398
##   100       0.9443508  0.36671246   0.7452521
##     5       7.3532663  0.19913854   7.2640762
##   100       0.9478911  0.36183902   0.7454192
##     5       7.3507120  0.21859354   7.2634405
##   100       0.9473812  0.36232249   0.7450512
##     5       7.3525154  0.20783616   7.2632700
##   100       0.9455770  0.36594481   0.7444526
##     5       7.3511650  0.23964975   7.2641233
##   100       0.9435887  0.36771850   0.7443631
##     5       7.3548749  0.20846273   7.2666966
##   100       0.9482229  0.36091980   0.7443135
##     5       7.3519577  0.23033416   7.2652852
##   100       0.9455863  0.36457989   0.7453936
##     5       7.3559929  0.23328465   7.2680590
##   100       0.9454358  0.36493203   0.7440074
##     5       7.3516588  0.23647437   7.2650483
##   100       0.9438987  0.36744112   0.7446161
##     5       7.3508741  0.21445377   7.2623883
##   100       0.9485535  0.36077035   0.7474174
##     5       7.3508520  0.23227093   7.2639131
##   100       0.9485001  0.36056428   0.7468176
##     5       7.3510520  0.21062149   7.2618391
##   100       0.9438562  0.36721379   0.7413362
##     5       7.3530315  0.23985710   7.2660301
##   100       0.9403896  0.37278762   0.7405696
##     5       7.3560201  0.22763607   7.2677059
##   100       0.9430299  0.36839250   0.7439065
##     5       7.3514000  0.23667186   7.2646346
##   100       0.9513613  0.35745163   0.7515477
##     5       7.3527223  0.19822739   7.2635920
##   100       0.9466114  0.36342183   0.7458340
##     5       7.3514000  0.23667186   7.2646346
##   100       0.9503111  0.35967077   0.7479946
##     5       7.3554199  0.18396097   7.2658790
##   100       0.9564161  0.35432923   0.7450818
##     5       7.3522255  0.22705676   7.2649324
##   100       0.9479063  0.36359160   0.7410360
##     5       7.3562211  0.19297406   7.2670307
##   100       0.9469368  0.36621658   0.7427649
##     5       7.3529135  0.23503994   7.2658440
##   100       0.9493044  0.36231533   0.7415809
##     5       7.3537160  0.22921512   7.2662192
##   100       0.9511616  0.36049147   0.7397102
##     5       7.3517823  0.23253250   7.2652772
##   100       0.9511574  0.36089084   0.7430282
##     5       7.3575816  0.22029989   7.2688204
##   100       0.9575420  0.35328429   0.7457137
##     5       7.3514828  0.23816839   7.2650398
##   100       0.9499244  0.36209036   0.7439341
##     5       7.3550148  0.19821205   7.2657074
##   100       0.9545613  0.35551047   0.7444723
##     5       7.3528191  0.21814429   7.2652466
##   100       0.9400782  0.37296868   0.7370430
##     5       7.3520337  0.19620364   7.2625246
##   100       0.9498820  0.36189694   0.7449508
##     5       7.3515407  0.23182870   7.2645835
##   100       0.9481968  0.36338380   0.7408602
##     5       7.3553215  0.22880796   7.2672995
##   100       0.9527628  0.35832919   0.7456367
##     5       7.3519577  0.23033416   7.2652852
##   100       0.9424120  0.36912328   0.7384223
##     5       7.3529391  0.21667874   7.2640689
##   100       0.9537793  0.35737365   0.7462401
##     5       7.3516588  0.23647437   7.2650483
##   100       0.9451765  0.36745314   0.7372774
##     5       7.3536180  0.18365210   7.2637284
##   100       0.9411997  0.37100539   0.7399410
##     5       7.3531164  0.23719190   7.2659924
##   100       0.9422393  0.36929825   0.7411609
##     5       7.3531040  0.18489464   7.2631962
##   100       0.9431700  0.36883678   0.7408186
##     5       7.3515902  0.22634257   7.2640504
##   100       0.9441399  0.36633043   0.7408307
##     5       7.3544732  0.23174394   7.2666211
##   100       0.9473425  0.36385882   0.7444427
##     5       7.3514000  0.23667186   7.2646346
##   100       0.9463556  0.36382293   0.7426908
##     5       7.3525752  0.21595258   7.2634092
##   100       0.9441583  0.36792623   0.7385782
##     5       7.3514000  0.23667186   7.2646346
##   100       0.9487993  0.36054672   0.7445112
##     5       7.3538418  0.20391333   7.2648988
##   100       0.9587272  0.35490847   0.7468828
##     5       7.3509630  0.22230397   7.2636934
##   100       0.9635671  0.34624267   0.7492380
##     5       7.3525863  0.21078057   7.2635719
##   100       0.9610144  0.35100169   0.7454040
##     5       7.3512061  0.20672777   7.2637884
##   100       0.9531718  0.35983343   0.7481056
##     5       7.3534034  0.20582523   7.2645721
##   100       0.9678443  0.34334713   0.7519692
##     5       7.3517823  0.23253250   7.2652772
##   100       0.9660695  0.34562129   0.7474841
##     5       7.3554301  0.21297188   7.2669374
##   100       0.9580066  0.35500906   0.7452928
##     5       7.3514828  0.23816839   7.2650398
##   100       0.9597324  0.35223041   0.7507978
##     5       7.3552977  0.20942635   7.2666248
##   100       0.9454523  0.36751049   0.7337913
##     5       7.3512198  0.23814312   7.2642916
##   100       0.9491771  0.36297473   0.7422838
##     5       7.3518888  0.22781524   7.2638228
##   100       0.9551372  0.35709450   0.7425491
##     5       7.3510632  0.22439877   7.2639087
##   100       0.9462421  0.36692946   0.7373856
##     5       7.3554550  0.23079032   7.2678087
##   100       0.9586155  0.35221371   0.7456378
##     5       7.3519577  0.23033416   7.2652852
##   100       0.9485273  0.36224750   0.7398107
##     5       7.3536221  0.21388600   7.2654817
##   100       0.9565683  0.35723918   0.7458403
##     5       7.3516588  0.23647437   7.2650483
##   100       0.9533088  0.35773112   0.7399751
##     5       7.3538492  0.19423176   7.2642930
##   100       0.9481140  0.36287010   0.7409248
##     5       7.3520559  0.23282997   7.2647923
##   100       0.9432489  0.36856371   0.7380205
##     5       7.3553160  0.22437083   7.2669433
##   100       0.9435104  0.36892142   0.7389938
##     5       7.3507045  0.22876496   7.2636031
##   100       0.9505445  0.35878001   0.7440750
##     5       7.3545356  0.20916759   7.2658461
##   100       0.9412705  0.37232629   0.7385716
##     5       7.3514000  0.23667186   7.2646346
##   100       0.9428100  0.36886997   0.7397426
##     5       7.3551725  0.21898143   7.2668561
##   100       0.9386839  0.37501786   0.7327559
##     5       7.3514000  0.23667186   7.2646346
##   100       0.9415948  0.36993006   0.7379886
##     5       2.3290085  0.27058085   2.0871099
##   100       0.9807494  0.33571363   0.7547568
##     5       2.3211838  0.26975722   2.0818811
##   100       0.9772689  0.33675423   0.7612742
##     5       2.3186803  0.27542903   2.0775348
##   100       0.9811673  0.33530793   0.7656917
##     5       2.3183613  0.28535168   2.0809648
##   100       0.9615118  0.35212032   0.7530860
##     5       2.3269634  0.25962717   2.0851538
##   100       0.9743232  0.34060678   0.7606105
##     5       2.3214108  0.29251519   2.0870296
##   100       0.9678641  0.34621723   0.7569181
##     5       2.3301098  0.26018883   2.0887404
##   100       0.9867931  0.32703655   0.7643883
##     5       2.3210805  0.29362546   2.0868893
##   100       0.9689197  0.34370394   0.7551272
##     5       2.3277664  0.26902294   2.0867419
##   100       0.9693145  0.34667154   0.7562780
##     5       2.3239112  0.28695147   2.0872726
##   100       0.9641565  0.34821817   0.7553384
##     5       2.3334239  0.26568285   2.0886109
##   100       0.9636921  0.35070142   0.7468970
##     5       2.3260304  0.27321746   2.0872491
##   100       0.9651664  0.34702462   0.7542961
##     5       2.3250797  0.26207959   2.0830861
##   100       0.9714091  0.34241211   0.7519374
##     5       2.3215987  0.29320142   2.0874349
##   100       0.9597409  0.35006910   0.7527654
##     5       2.3290939  0.27316662   2.0884865
##   100       0.9661536  0.35080762   0.7600647
##     5       2.3212054  0.29435333   2.0872257
##   100       0.9586428  0.35292399   0.7527586
##     5       2.3231028  0.27439007   2.0821750
##   100       0.9679045  0.34388579   0.7567852
##     5       2.3289913  0.26951646   2.0890706
##   100       0.9529743  0.35575091   0.7504652
##     5       2.3255064  0.25297130   2.0790709
##   100       0.9601993  0.35112645   0.7506044
##     5       2.3196500  0.28663493   2.0810304
##   100       0.9560167  0.35243057   0.7487321
##     5       2.3255362  0.26890447   2.0850048
##   100       0.9694091  0.34199280   0.7604642
##     5       2.3207596  0.28663923   2.0854221
##   100       0.9527549  0.35407891   0.7515966
##     5       2.3280319  0.27817684   2.0886915
##   100       0.9730782  0.33628719   0.7580379
##     5       2.3203663  0.28779114   2.0852129
##   100       0.9620411  0.34331457   0.7533385
##     5       2.3266259  0.27778523   2.0878182
##   100       1.0213717  0.30196758   0.7858523
##     5       2.3176590  0.28581152   2.0824013
##   100       0.9983731  0.31967018   0.7777987
##     5       2.3256793  0.29301417   2.0919115
##   100       1.0157683  0.30932004   0.7902023
##     5       2.3237905  0.29906639   2.0910332
##   100       0.9981650  0.31899296   0.7729769
##     5       2.3319631  0.28118826   2.0980084
##   100       1.0118510  0.31483512   0.7825935
##     5       2.3240279  0.28826447   2.0937522
##   100       1.0140551  0.30461821   0.7887163
##     5       2.3271020  0.29183368   2.0955712
##   100       1.0211173  0.30331210   0.7862692
##     5       2.3187088  0.30106624   2.0908690
##   100       0.9983463  0.32145055   0.7731137
##     5       2.3292686  0.29289859   2.0957779
##   100       1.0005144  0.31560752   0.7807425
##     5       2.3177345  0.29370523   2.0822386
##   100       0.9800780  0.33327141   0.7620533
##     5       2.3334875  0.27918430   2.0952135
##   100       1.0097131  0.31067332   0.7842428
##     5       2.3162577  0.29518121   2.0847007
##   100       0.9765861  0.33617609   0.7599016
##     5       2.3228781  0.27737750   2.0876965
##   100       0.9980598  0.32094518   0.7768272
##     5       2.3199395  0.29336988   2.0903969
##   100       0.9673477  0.34626773   0.7536354
##     5       2.3318505  0.28558239   2.0992370
##   100       0.9947164  0.32612115   0.7694702
##     5       2.3183597  0.30205656   2.0902894
##   100       0.9689379  0.34174255   0.7529529
##     5       2.3308099  0.28537186   2.0954507
##   100       0.9659155  0.34780366   0.7537462
##     5       2.3281885  0.28582639   2.0912271
##   100       0.9617952  0.34701695   0.7512393
##     5       2.3313626  0.27817107   2.0939915
##   100       0.9658659  0.35022457   0.7552286
##     5       2.3197297  0.29420726   2.0869300
##   100       0.9576736  0.35106617   0.7468941
##     5       2.3278045  0.27517500   2.0918246
##   100       0.9654673  0.35005150   0.7528583
##     5       2.3148446  0.29347104   2.0834364
##   100       0.9627346  0.34361461   0.7509519
##     5       2.3280816  0.28153633   2.0932707
##   100       0.9735622  0.34082259   0.7615553
##     5       2.3184829  0.29309473   2.0875213
##   100       0.9583072  0.34927710   0.7494729
##     5       2.3350786  0.27257270   2.0998032
##   100       1.0531830  0.27294183   0.8167890
##     5       2.3269757  0.30399474   2.1008050
##   100       1.0174545  0.30415257   0.7883645
##     5       2.3294180  0.27704682   2.0921520
##   100       1.0339639  0.29357216   0.7981258
##     5       2.3270274  0.28676148   2.0943206
##   100       1.0020465  0.32187734   0.7772423
##     5       2.3366809  0.27912342   2.1057075
##   100       1.0380983  0.29203073   0.8063551
##     5       2.3263340  0.28887536   2.0974577
##   100       1.0302093  0.29021769   0.8021509
##     5       2.3322897  0.30723572   2.1048086
##   100       1.0529501  0.27901996   0.8173337
##     5       2.3225308  0.29994883   2.0959503
##   100       1.0157979  0.30270643   0.7960660
##     5       2.3372716  0.26293625   2.0987800
##   100       1.0143647  0.30023348   0.7890216
##     5       2.3247363  0.28560350   2.0917763
##   100       0.9790514  0.33391773   0.7614866
##     5       2.3334361  0.27034903   2.0952088
##   100       1.0156584  0.30068983   0.7984868
##     5       2.3197936  0.29550787   2.0878880
##   100       0.9858484  0.32818729   0.7712411
##     5       2.3291507  0.28676470   2.0977460
##   100       1.0271217  0.29481285   0.7935624
##     5       2.3199981  0.29575529   2.0913360
##   100       0.9786451  0.33242072   0.7611091
##     5       2.3260863  0.29177178   2.0965048
##   100       1.0176273  0.30655444   0.7915314
##     5       2.3195073  0.30693754   2.0933785
##   100       0.9817435  0.32860308   0.7622255
##     5       2.3289346  0.26848692   2.0909054
##   100       0.9676350  0.34769607   0.7542693
##     5       2.3256535  0.26810503   2.0876490
##   100       0.9552859  0.35675179   0.7501941
##     5       2.3260407  0.27099568   2.0858368
##   100       0.9685659  0.34612766   0.7560081
##     5       2.3170527  0.29360498   2.0834059
##   100       0.9669772  0.34190677   0.7530561
##     5       2.3159564  0.29056738   2.0825692
##   100       0.9726918  0.34350952   0.7569778
##     5       2.3152445  0.29509314   2.0849202
##   100       0.9551702  0.35503605   0.7450100
##     5       2.3259640  0.29686713   2.0939425
##   100       0.9808185  0.33245953   0.7644920
##     5       2.3198609  0.29486809   2.0897090
##   100       0.9559349  0.35400751   0.7488271
## 
## RMSE was used to select the optimal model using the smallest value.
## The final values used for the model were nrounds = 100, max_depth = 7, eta
##  = 0.1, gamma = 3, colsample_bytree = 1, min_child_weight = 3 and subsample
##  = 0.8.
plot(varImp(xgb_tune, scale = F), scales = list(y = list(cex = .95)))

# Hacer predicciones en el conjunto de prueba
test_results$xgb <- predict(xgb_tune, testing)

# Evaluar el modelo Gradient Boosting
xgb_metrics <- postResample(pred = test_results$xgb, obs = testing$average_grade)
print(xgb_metrics)
##      RMSE  Rsquared       MAE 
## 0.9851380 0.3585118 0.7387951

The Gradient Boosting model outperforms others in terms of predictive accuracy and will be used as the final model for our prediction task. This aligns with the power of machine learning to capture complex relationships in data. Its RMSE (0.984) is relatively lower compared to other models, indicating that it makes predictions with smaller errors. Its R-squared (0.359) means that the model explains around 35.9% of the variance in average_grade, which is better than many of the other models we tested. On its part, the MAE (0.735) is also lower.

The model identifies academic performance metrics (average evaluations, admission grades, and prior grades) as the strongest predictors of outcomes, aligning with expectations in educational models. Socioeconomic factors like GDP and unemployment rates show moderate influence, highlighting the role of broader economic conditions. Demographic variables such as age at enrollment and parental education (e.g., mother’s higher education) also contribute meaningfully. In contrast, variables related to some maternal occupations or special needs show negligible impact.

Neural Network

set.seed(123)
# Definir la grilla de hiperparámetros (ajustar número de neuronas)
nn_grid <- expand.grid(size = c(2, 4, 6),  # Número de neuronas en la capa oculta
                       decay = c(0.1, 0.01))  # Regularización para evitar overfitting

# Entrenar la red neuronal
set.seed(123)
nn_tune <- train(average_grade ~ ., 
                 data = training, 
                 method = "nnet",
                 preProc = c('scale', 'center'),
                 tuneGrid = nn_grid,
                 maxit = 200,  # Iteraciones limitadas para evitar largos tiempos
                 trControl = ctrl,
                 linout = TRUE)  # Salida lineal porque estamos haciendo regresión
## # weights:  87
## initial  value 237820.476727 
## iter  10 value 2350.776089
## iter  20 value 2307.400647
## iter  30 value 2222.196323
## iter  40 value 2114.013174
## iter  50 value 2014.907656
## iter  60 value 1913.347050
## iter  70 value 1844.628785
## iter  80 value 1816.883577
## iter  90 value 1809.232026
## iter 100 value 1785.296106
## iter 110 value 1717.212111
## iter 120 value 1635.527669
## iter 130 value 1579.270292
## iter 140 value 1496.576090
## iter 150 value 1443.228012
## iter 160 value 1385.396615
## iter 170 value 1358.334664
## iter 180 value 1342.230280
## iter 190 value 1317.233333
## iter 200 value 1304.783574
## final  value 1304.783574 
## stopped after 200 iterations
## # weights:  173
## initial  value 272020.366490 
## iter  10 value 14140.578871
## iter  20 value 2586.976644
## iter  30 value 2447.584669
## iter  40 value 2340.722382
## iter  50 value 2294.850819
## iter  60 value 2229.936361
## iter  70 value 2139.181571
## iter  80 value 2058.999793
## iter  90 value 2012.469875
## iter 100 value 1985.341327
## iter 110 value 1969.025601
## iter 120 value 1947.807048
## iter 130 value 1917.750641
## iter 140 value 1897.801901
## iter 150 value 1859.339278
## iter 160 value 1726.388297
## iter 170 value 1620.394228
## iter 180 value 1551.739888
## iter 190 value 1481.964652
## iter 200 value 1414.553048
## final  value 1414.553048 
## stopped after 200 iterations
## # weights:  259
## initial  value 249723.826980 
## iter  10 value 1645.230129
## iter  20 value 1357.904984
## iter  30 value 1265.581212
## iter  40 value 1194.048116
## iter  50 value 1159.281293
## iter  60 value 1140.860770
## iter  70 value 1116.086248
## iter  80 value 1098.646222
## iter  90 value 1086.190795
## iter 100 value 1080.162657
## iter 110 value 1077.269401
## iter 120 value 1074.127665
## iter 130 value 1070.875735
## iter 140 value 1069.584315
## iter 150 value 1067.510445
## iter 160 value 1062.956209
## iter 170 value 1057.827144
## iter 180 value 1050.853020
## iter 190 value 1047.726246
## iter 200 value 1045.553845
## final  value 1045.553845 
## stopped after 200 iterations
## # weights:  87
## initial  value 247351.910950 
## iter  10 value 2188.216653
## iter  20 value 2104.266129
## iter  30 value 2051.225336
## iter  40 value 1963.559750
## iter  50 value 1878.905130
## iter  60 value 1863.703167
## iter  70 value 1841.497989
## iter  80 value 1818.649999
## iter  90 value 1789.338489
## iter 100 value 1772.260091
## iter 110 value 1764.923482
## iter 120 value 1757.185815
## iter 130 value 1751.193703
## iter 140 value 1743.099645
## iter 150 value 1741.368658
## iter 160 value 1740.097575
## iter 170 value 1684.024465
## iter 180 value 1656.054353
## iter 190 value 1645.448354
## iter 200 value 1625.682017
## final  value 1625.682017 
## stopped after 200 iterations
## # weights:  173
## initial  value 245397.739162 
## iter  10 value 2124.699309
## iter  20 value 1583.050833
## iter  30 value 1443.665599
## iter  40 value 1396.240539
## iter  50 value 1337.975729
## iter  60 value 1300.679313
## iter  70 value 1281.014032
## iter  80 value 1270.360210
## iter  90 value 1264.105859
## iter 100 value 1260.264130
## iter 110 value 1256.396599
## iter 120 value 1251.006388
## iter 130 value 1245.000352
## iter 140 value 1239.865844
## iter 150 value 1234.558365
## iter 160 value 1230.778533
## iter 170 value 1225.556187
## iter 180 value 1220.505837
## iter 190 value 1216.879496
## iter 200 value 1214.299603
## final  value 1214.299603 
## stopped after 200 iterations
## # weights:  259
## initial  value 259297.361350 
## iter  10 value 1441.176752
## iter  20 value 1268.686374
## iter  30 value 1221.814236
## iter  40 value 1175.745084
## iter  50 value 1135.875088
## iter  60 value 1101.100467
## iter  70 value 1062.375339
## iter  80 value 1041.393113
## iter  90 value 1025.091171
## iter 100 value 1009.718958
## iter 110 value 1000.334526
## iter 120 value 992.393380
## iter 130 value 983.359363
## iter 140 value 976.988724
## iter 150 value 971.512187
## iter 160 value 966.540041
## iter 170 value 962.286217
## iter 180 value 959.860263
## iter 190 value 957.786671
## iter 200 value 955.250563
## final  value 955.250563 
## stopped after 200 iterations
## # weights:  87
## initial  value 252089.389752 
## iter  10 value 2220.349465
## iter  20 value 2178.479354
## iter  30 value 2141.802450
## iter  40 value 2096.421084
## iter  50 value 1922.436634
## iter  60 value 1858.598184
## iter  70 value 1814.627925
## iter  80 value 1740.489927
## iter  90 value 1667.817547
## iter 100 value 1630.577802
## iter 110 value 1612.953772
## iter 120 value 1591.423945
## iter 130 value 1571.396719
## iter 140 value 1560.629937
## iter 150 value 1554.959080
## iter 160 value 1536.871902
## iter 170 value 1512.852581
## iter 180 value 1429.985235
## iter 190 value 1388.007037
## iter 200 value 1358.155131
## final  value 1358.155131 
## stopped after 200 iterations
## # weights:  173
## initial  value 268222.067869 
## iter  10 value 2017.809868
## iter  20 value 1496.272958
## iter  30 value 1394.838091
## iter  40 value 1334.802744
## iter  50 value 1290.859880
## iter  60 value 1258.046094
## iter  70 value 1238.153369
## iter  80 value 1230.498686
## iter  90 value 1224.655796
## iter 100 value 1217.917434
## iter 110 value 1210.842548
## iter 120 value 1203.964221
## iter 130 value 1196.056167
## iter 140 value 1193.399792
## iter 150 value 1191.975481
## iter 160 value 1191.617604
## iter 170 value 1190.872172
## iter 180 value 1187.178740
## iter 190 value 1182.310925
## iter 200 value 1179.891672
## final  value 1179.891672 
## stopped after 200 iterations
## # weights:  259
## initial  value 260198.182216 
## iter  10 value 1600.029487
## iter  20 value 1315.603332
## iter  30 value 1246.203859
## iter  40 value 1190.232102
## iter  50 value 1163.203807
## iter  60 value 1116.262583
## iter  70 value 1082.902790
## iter  80 value 1067.313988
## iter  90 value 1059.822585
## iter 100 value 1053.378526
## iter 110 value 1046.612232
## iter 120 value 1039.780076
## iter 130 value 1034.886333
## iter 140 value 1031.577033
## iter 150 value 1029.244952
## iter 160 value 1027.368257
## iter 170 value 1025.122347
## iter 180 value 1022.424781
## iter 190 value 1018.604212
## iter 200 value 1015.540256
## final  value 1015.540256 
## stopped after 200 iterations
## # weights:  87
## initial  value 245500.807629 
## iter  10 value 2441.121626
## iter  20 value 2337.212077
## iter  30 value 2159.243331
## iter  40 value 1952.834989
## iter  50 value 1841.530432
## iter  60 value 1710.189187
## iter  70 value 1633.370643
## iter  80 value 1591.236324
## iter  90 value 1571.402909
## iter 100 value 1554.634268
## iter 110 value 1546.349334
## iter 120 value 1542.797765
## iter 130 value 1541.504785
## iter 140 value 1539.625949
## iter 150 value 1533.089646
## iter 160 value 1523.142903
## iter 170 value 1518.090889
## iter 180 value 1515.509707
## iter 190 value 1512.132403
## iter 200 value 1507.775706
## final  value 1507.775706 
## stopped after 200 iterations
## # weights:  173
## initial  value 276192.273080 
## iter  10 value 1884.662108
## iter  20 value 1438.575377
## iter  30 value 1322.376980
## iter  40 value 1269.389723
## iter  50 value 1239.457192
## iter  60 value 1231.151011
## iter  70 value 1215.776984
## iter  80 value 1207.624675
## iter  90 value 1202.614993
## iter 100 value 1196.010951
## iter 110 value 1191.964983
## iter 120 value 1187.031442
## iter 130 value 1183.120260
## iter 140 value 1181.088167
## iter 150 value 1179.653466
## iter 160 value 1177.342967
## iter 170 value 1174.835879
## iter 180 value 1170.189252
## iter 190 value 1165.503831
## iter 200 value 1159.603489
## final  value 1159.603489 
## stopped after 200 iterations
## # weights:  259
## initial  value 258118.429694 
## iter  10 value 1446.279559
## iter  20 value 1243.998367
## iter  30 value 1168.938693
## iter  40 value 1127.331725
## iter  50 value 1104.300353
## iter  60 value 1071.178682
## iter  70 value 1037.550913
## iter  80 value 1011.041939
## iter  90 value 994.592888
## iter 100 value 986.779261
## iter 110 value 980.878100
## iter 120 value 977.174959
## iter 130 value 974.817231
## iter 140 value 972.472102
## iter 150 value 969.654841
## iter 160 value 966.953613
## iter 170 value 963.711371
## iter 180 value 960.896485
## iter 190 value 957.827469
## iter 200 value 954.957488
## final  value 954.957488 
## stopped after 200 iterations
## # weights:  87
## initial  value 239449.230768 
## iter  10 value 2015.203617
## iter  20 value 1963.922072
## iter  30 value 1914.622217
## iter  40 value 1759.141871
## iter  50 value 1713.601194
## iter  60 value 1652.785027
## iter  70 value 1601.272229
## iter  80 value 1575.862981
## iter  90 value 1561.270704
## iter 100 value 1555.267244
## iter 110 value 1541.851470
## iter 120 value 1498.533110
## iter 130 value 1458.864817
## iter 140 value 1436.298359
## iter 150 value 1417.064501
## iter 160 value 1364.512321
## iter 170 value 1346.758687
## iter 180 value 1331.674699
## iter 190 value 1324.120797
## iter 200 value 1317.982970
## final  value 1317.982970 
## stopped after 200 iterations
## # weights:  173
## initial  value 245460.173350 
## iter  10 value 1788.938170
## iter  20 value 1473.882105
## iter  30 value 1426.309834
## iter  40 value 1386.116250
## iter  50 value 1362.345768
## iter  60 value 1342.886382
## iter  70 value 1333.825071
## iter  80 value 1320.850176
## iter  90 value 1312.695213
## iter 100 value 1305.092014
## iter 110 value 1301.534319
## iter 120 value 1299.006480
## iter 130 value 1294.031689
## iter 140 value 1284.020808
## iter 150 value 1280.351500
## iter 160 value 1278.046653
## iter 170 value 1275.093658
## iter 180 value 1268.998793
## iter 190 value 1261.136461
## iter 200 value 1253.504330
## final  value 1253.504330 
## stopped after 200 iterations
## # weights:  259
## initial  value 226054.802229 
## iter  10 value 1570.498344
## iter  20 value 1268.566659
## iter  30 value 1187.861584
## iter  40 value 1153.734069
## iter  50 value 1132.926187
## iter  60 value 1105.725927
## iter  70 value 1071.772476
## iter  80 value 1048.027395
## iter  90 value 1032.943423
## iter 100 value 1023.500592
## iter 110 value 1018.258695
## iter 120 value 1014.735057
## iter 130 value 1010.016251
## iter 140 value 1006.520919
## iter 150 value 1004.453549
## iter 160 value 1002.881994
## iter 170 value 1001.134920
## iter 180 value 998.916604
## iter 190 value 995.700146
## iter 200 value 993.178113
## final  value 993.178113 
## stopped after 200 iterations
## # weights:  87
## initial  value 269674.949016 
## iter  10 value 2145.121641
## iter  20 value 2101.036135
## iter  30 value 2085.533612
## iter  40 value 2013.080709
## iter  50 value 1919.022266
## iter  60 value 1854.370960
## iter  70 value 1773.684543
## iter  80 value 1668.523872
## iter  90 value 1608.029034
## iter 100 value 1548.082536
## iter 110 value 1499.356499
## iter 120 value 1480.985152
## iter 130 value 1457.078124
## iter 140 value 1440.792365
## iter 150 value 1430.319135
## iter 160 value 1419.636178
## iter 170 value 1407.691265
## iter 180 value 1395.316192
## iter 190 value 1372.953193
## iter 200 value 1344.889080
## final  value 1344.889080 
## stopped after 200 iterations
## # weights:  173
## initial  value 232511.534163 
## iter  10 value 3262.145541
## iter  20 value 1737.067937
## iter  30 value 1493.282543
## iter  40 value 1406.532064
## iter  50 value 1371.547193
## iter  60 value 1340.250028
## iter  70 value 1320.942184
## iter  80 value 1316.565206
## iter  90 value 1315.314640
## iter 100 value 1314.133404
## iter 110 value 1308.155464
## iter 120 value 1303.804910
## iter 130 value 1302.074494
## iter 140 value 1300.084899
## iter 150 value 1299.296112
## iter 160 value 1298.054783
## iter 170 value 1295.758155
## iter 180 value 1290.193409
## iter 190 value 1284.118271
## iter 200 value 1282.676418
## final  value 1282.676418 
## stopped after 200 iterations
## # weights:  259
## initial  value 273981.334440 
## iter  10 value 1466.560275
## iter  20 value 1275.372495
## iter  30 value 1196.340932
## iter  40 value 1147.463694
## iter  50 value 1112.559473
## iter  60 value 1073.232401
## iter  70 value 1034.663065
## iter  80 value 1013.462550
## iter  90 value 1004.743042
## iter 100 value 995.531306
## iter 110 value 990.078363
## iter 120 value 986.947244
## iter 130 value 984.262752
## iter 140 value 982.009694
## iter 150 value 980.189060
## iter 160 value 977.862201
## iter 170 value 974.492496
## iter 180 value 971.301404
## iter 190 value 969.159206
## iter 200 value 966.930527
## final  value 966.930527 
## stopped after 200 iterations
## # weights:  87
## initial  value 251756.678049 
## iter  10 value 2828.919503
## iter  20 value 2455.233281
## iter  30 value 2073.352030
## iter  40 value 1996.294507
## iter  50 value 1861.676026
## iter  60 value 1718.189396
## iter  70 value 1648.411727
## iter  80 value 1614.921901
## iter  90 value 1588.322994
## iter 100 value 1566.930732
## iter 110 value 1547.116455
## iter 120 value 1524.399694
## iter 130 value 1512.264983
## iter 140 value 1466.479393
## iter 150 value 1458.393637
## iter 160 value 1438.882618
## iter 170 value 1422.177239
## iter 180 value 1405.042327
## iter 190 value 1385.798708
## iter 200 value 1381.063597
## final  value 1381.063597 
## stopped after 200 iterations
## # weights:  173
## initial  value 267946.605236 
## iter  10 value 1794.443069
## iter  20 value 1513.860004
## iter  30 value 1432.393961
## iter  40 value 1349.232332
## iter  50 value 1307.764978
## iter  60 value 1295.675083
## iter  70 value 1279.105575
## iter  80 value 1263.461643
## iter  90 value 1253.327400
## iter 100 value 1242.446914
## iter 110 value 1229.985926
## iter 120 value 1221.029249
## iter 130 value 1210.435666
## iter 140 value 1190.701795
## iter 150 value 1181.065343
## iter 160 value 1175.671164
## iter 170 value 1171.748686
## iter 180 value 1170.415472
## iter 190 value 1169.878437
## iter 200 value 1168.940392
## final  value 1168.940392 
## stopped after 200 iterations
## # weights:  259
## initial  value 303576.752333 
## iter  10 value 1635.313347
## iter  20 value 1297.547085
## iter  30 value 1219.422293
## iter  40 value 1185.093431
## iter  50 value 1139.887136
## iter  60 value 1110.168042
## iter  70 value 1092.016044
## iter  80 value 1077.889590
## iter  90 value 1068.895721
## iter 100 value 1061.059341
## iter 110 value 1053.871925
## iter 120 value 1050.683613
## iter 130 value 1048.428781
## iter 140 value 1046.294318
## iter 150 value 1044.559974
## iter 160 value 1043.220123
## iter 170 value 1042.164915
## iter 180 value 1041.488410
## iter 190 value 1039.899955
## iter 200 value 1038.568110
## final  value 1038.568110 
## stopped after 200 iterations
## # weights:  87
## initial  value 241503.896535 
## iter  10 value 2173.702744
## iter  20 value 2142.718542
## iter  30 value 2130.913977
## iter  40 value 2094.206441
## iter  50 value 1922.691106
## iter  60 value 1783.475278
## iter  70 value 1682.391303
## iter  80 value 1512.014307
## iter  90 value 1438.447168
## iter 100 value 1369.548192
## iter 110 value 1347.116993
## iter 120 value 1332.706132
## iter 130 value 1320.424805
## iter 140 value 1311.334061
## iter 150 value 1302.578738
## iter 160 value 1298.273975
## iter 170 value 1295.097276
## iter 180 value 1293.823865
## iter 190 value 1293.072467
## iter 200 value 1292.477825
## final  value 1292.477825 
## stopped after 200 iterations
## # weights:  173
## initial  value 250355.694192 
## iter  10 value 2471.166292
## iter  20 value 2097.779226
## iter  30 value 1990.682592
## iter  40 value 1814.986403
## iter  50 value 1650.097076
## iter  60 value 1555.623909
## iter  70 value 1502.498734
## iter  80 value 1448.374533
## iter  90 value 1399.953627
## iter 100 value 1372.904718
## iter 110 value 1348.023042
## iter 120 value 1336.047892
## iter 130 value 1326.113045
## iter 140 value 1319.352085
## iter 150 value 1312.207475
## iter 160 value 1306.926650
## iter 170 value 1299.882361
## iter 180 value 1297.862747
## iter 190 value 1293.468985
## iter 200 value 1288.611913
## final  value 1288.611913 
## stopped after 200 iterations
## # weights:  259
## initial  value 220631.032001 
## iter  10 value 1600.988431
## iter  20 value 1328.260261
## iter  30 value 1245.623342
## iter  40 value 1199.725354
## iter  50 value 1165.181119
## iter  60 value 1135.322706
## iter  70 value 1110.401778
## iter  80 value 1074.953849
## iter  90 value 1048.398917
## iter 100 value 1033.603186
## iter 110 value 1012.160702
## iter 120 value 997.659510
## iter 130 value 991.228386
## iter 140 value 985.438841
## iter 150 value 979.213425
## iter 160 value 976.362076
## iter 170 value 974.225868
## iter 180 value 970.479541
## iter 190 value 967.588085
## iter 200 value 965.855965
## final  value 965.855965 
## stopped after 200 iterations
## # weights:  87
## initial  value 255107.659860 
## iter  10 value 2071.264018
## iter  20 value 1990.028777
## iter  30 value 1876.394882
## iter  40 value 1790.315420
## iter  50 value 1700.008958
## iter  60 value 1642.295744
## iter  70 value 1562.503753
## iter  80 value 1520.163748
## iter  90 value 1485.304011
## iter 100 value 1476.298663
## iter 110 value 1470.438779
## iter 120 value 1456.756679
## iter 130 value 1389.234649
## iter 140 value 1344.382082
## iter 150 value 1328.610911
## iter 160 value 1303.124079
## iter 170 value 1288.736257
## iter 180 value 1276.888112
## iter 190 value 1272.355517
## iter 200 value 1268.834302
## final  value 1268.834302 
## stopped after 200 iterations
## # weights:  173
## initial  value 267432.727539 
## iter  10 value 1630.861880
## iter  20 value 1459.563052
## iter  30 value 1398.331807
## iter  40 value 1339.890858
## iter  50 value 1308.854068
## iter  60 value 1283.337485
## iter  70 value 1266.050060
## iter  80 value 1253.116168
## iter  90 value 1238.457179
## iter 100 value 1231.093568
## iter 110 value 1224.801055
## iter 120 value 1217.470703
## iter 130 value 1210.591347
## iter 140 value 1203.767299
## iter 150 value 1198.191560
## iter 160 value 1192.279000
## iter 170 value 1187.878779
## iter 180 value 1182.790572
## iter 190 value 1177.564684
## iter 200 value 1174.429874
## final  value 1174.429874 
## stopped after 200 iterations
## # weights:  259
## initial  value 304652.783737 
## iter  10 value 1437.478914
## iter  20 value 1261.071802
## iter  30 value 1212.419023
## iter  40 value 1162.944852
## iter  50 value 1126.551319
## iter  60 value 1101.771491
## iter  70 value 1083.711558
## iter  80 value 1068.962376
## iter  90 value 1053.304585
## iter 100 value 1040.833914
## iter 110 value 1029.941422
## iter 120 value 1019.109574
## iter 130 value 1012.370254
## iter 140 value 1008.733116
## iter 150 value 1004.662377
## iter 160 value 1001.277303
## iter 170 value 999.366120
## iter 180 value 997.982917
## iter 190 value 996.568826
## iter 200 value 995.596940
## final  value 995.596940 
## stopped after 200 iterations
## # weights:  87
## initial  value 254155.103841 
## iter  10 value 2177.360706
## iter  20 value 2083.383978
## iter  30 value 2042.493458
## iter  40 value 2015.911443
## iter  50 value 1854.797340
## iter  60 value 1663.456041
## iter  70 value 1616.411290
## iter  80 value 1587.460817
## iter  90 value 1571.387368
## iter 100 value 1545.130348
## iter 110 value 1498.208419
## iter 120 value 1453.184569
## iter 130 value 1427.596342
## iter 140 value 1360.623977
## iter 150 value 1319.305591
## iter 160 value 1313.183928
## iter 170 value 1309.018775
## iter 180 value 1308.730494
## iter 190 value 1305.344569
## iter 200 value 1288.631874
## final  value 1288.631874 
## stopped after 200 iterations
## # weights:  173
## initial  value 267362.094474 
## iter  10 value 5934.367918
## iter  20 value 3072.810546
## iter  30 value 2611.974463
## iter  40 value 2343.330082
## iter  50 value 2280.269856
## iter  60 value 2223.018469
## iter  70 value 2184.823580
## iter  80 value 2163.351487
## iter  90 value 2151.128334
## iter 100 value 2128.312826
## iter 110 value 2089.519203
## iter 120 value 2022.758222
## iter 130 value 1984.908964
## iter 140 value 1945.077959
## iter 150 value 1905.632525
## iter 160 value 1859.549025
## iter 170 value 1742.374718
## iter 180 value 1643.362453
## iter 190 value 1553.737204
## iter 200 value 1466.304537
## final  value 1466.304537 
## stopped after 200 iterations
## # weights:  259
## initial  value 231741.865050 
## iter  10 value 1484.027792
## iter  20 value 1232.314903
## iter  30 value 1171.634569
## iter  40 value 1136.654218
## iter  50 value 1115.013913
## iter  60 value 1098.825998
## iter  70 value 1085.033384
## iter  80 value 1056.603050
## iter  90 value 1036.976878
## iter 100 value 1023.432747
## iter 110 value 1014.892193
## iter 120 value 1008.198477
## iter 130 value 1002.499916
## iter 140 value 998.467955
## iter 150 value 993.511577
## iter 160 value 990.175011
## iter 170 value 987.430165
## iter 180 value 984.292670
## iter 190 value 981.713162
## iter 200 value 979.893841
## final  value 979.893841 
## stopped after 200 iterations
## # weights:  87
## initial  value 312724.618334 
## iter  10 value 3069.062659
## iter  20 value 2903.729961
## iter  30 value 2720.469893
## iter  40 value 2513.434131
## iter  50 value 2348.812804
## iter  60 value 2230.006055
## iter  70 value 2127.214669
## iter  80 value 2034.021144
## iter  90 value 1960.283168
## iter 100 value 1871.046436
## iter 110 value 1832.036363
## iter 120 value 1811.569464
## iter 130 value 1792.748090
## iter 140 value 1749.870891
## iter 150 value 1711.509518
## iter 160 value 1703.073659
## iter 170 value 1691.191650
## iter 180 value 1686.121948
## iter 190 value 1685.393017
## iter 200 value 1684.541189
## final  value 1684.541189 
## stopped after 200 iterations
# Ver resultados
print(nn_tune)
## Neural Network 
## 
## 1938 samples
##   41 predictor
## 
## Pre-processing: scaled (41), centered (41) 
## Resampling: Cross-Validated (5 fold, repeated 1 times) 
## Summary of sample sizes: 1551, 1550, 1550, 1550, 1551 
## Resampling results across tuning parameters:
## 
##   size  decay  RMSE      Rsquared   MAE      
##   2     0.01   1.085031  0.2162995  0.8225768
##   2     0.10   1.019160  0.2800496  0.7963020
##   4     0.01   1.189801  0.1685484  0.8824915
##   4     0.10   1.043455  0.2605620  0.8212750
##   6     0.01   1.094418  0.2417681  0.8641810
##   6     0.10   1.106200  0.2266146  0.8749263
## 
## RMSE was used to select the optimal model using the smallest value.
## The final values used for the model were size = 2 and decay = 0.1.
plot(nn_tune)

# Hacer predicciones en el conjunto de prueba
test_results$nn <- predict(nn_tune, testing)

# Evaluar el modelo
nn_metrics <- postResample(pred = test_results$nn, obs = testing$average_grade)
print(nn_metrics)
##      RMSE  Rsquared       MAE 
## 1.0631244 0.2662278 0.7906771

This last model predicts worse than Gradient Boosting.

Let’s put together the results obtained in this part.

# Crear un data frame con los resultados de cada modelo
model_comparison <- data.frame(
  Model = c("KNN", "Random Forest", "Decision Tree", 
            "XGBoost", "Neural Network"),
  RMSE = c(knn_metrics[1], rf_metrics[1], dt_metrics[1], 
           xgb_metrics[1], nn_metrics[1]),
  R2 = c(knn_metrics[2], rf_metrics[2], dt_metrics[2], 
         xgb_metrics[2], nn_metrics[2]),
  MAE = c(knn_metrics[3], rf_metrics[3], dt_metrics[3], 
          xgb_metrics[3], nn_metrics[3])
)

# Mostrar tabla de comparación
print(model_comparison)
##            Model     RMSE        R2       MAE
## 1            KNN 1.149084 0.1353695 0.8898548
## 2  Random Forest 1.009877 0.3317068 0.7651697
## 3  Decision Tree 1.121815 0.1720713 0.8738138
## 4        XGBoost 0.985138 0.3585118 0.7387951
## 5 Neural Network 1.063124 0.2662278 0.7906771

Ensamble model

To conclude our analysis, we will create an ensemble model combining the three best-performing models:Gradient Boosting, Random Forest and Stepwise Regression. The goal of this ensemble is to leverage the strengths of each model and see if the combination improves the overall prediction accuracy.

# Hacer predicciones individuales
test_results$stepwise <- predict(stepwise_model, testing)
test_results$rf <- predict(rf_tune, testing)
test_results$xgb <- predict(xgb_tune, testing)

# Hacer el ensemble promediando las predicciones
test_results$ensemble_avg <- (test_results$stepwise + test_results$rf + 
                                test_results$xgb) / 3

# Evaluar el modelo ensemble
ensemble_metrics <- postResample(pred = test_results$ensemble_avg, 
                                 obs = testing$average_grade)
print(ensemble_metrics)
##      RMSE  Rsquared       MAE 
## 0.9974109 0.3455710 0.7528790

The ensemble method, in this case, does not provide a major improvement. Gradient Boosting alone is better

As a final conclusion for this part we can say that it seems that the variables in the dataset do not fully explain the variability average grade. Our model’s performance has been limited in this second part, even if we tried several techniques, so maybe the features are not the most relevant or don’t capture the underlying factors that influence students’ average grade during their first year at Univesity.

Bibliography:

  • Davis-Kean, P. E. (2005). The influence of parent education and family income on child achievement: The indirect role of parental expectations and the home environment. Journal of Family Psychology, 19(2), 294–304.
  • Fan, X., & Chen, M. (2001). Parental involvement and students’ academic achievement: A meta-analysis. Educational Psychology Review, 13(1), 1–22.
  • Realinho, V., Vieira Martins, M., Machado, J., & Baptista, L. (2021). Predict Students’ Dropout and Academic Success [Dataset]. UCI Machine Learning Repository.